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‘f’ is a real function such that f(x + y) = f(xy) for all real values of x and y. If f(–7) = 7, then the value of f(–49) + f(49) is
(2014)
  • a)
    7
  • b)
    14
  • c)
    0
  • d)
    49
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
‘f’ is a real function such that f(x + y) = f(xy) for all ...
Let us assume f(0) = K, where 'K' is a constant.
Then, f(0 + y) = f(0.y) = f(0) = K
and  f(x + 0) = f(x.0) = f(0) = K.
This proves that the function is a constant function.
Thus, the value of
f(–49) = f (49) = 7
Hence, f(–49) + f(49) = 14.
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Most Upvoted Answer
‘f’ is a real function such that f(x + y) = f(xy) for all ...
Let us assume f(0) = K, where 'K' is a constant.
Then, f(0 + y) = f(0.y) = f(0) = K
and  f(x + 0) = f(x.0) = f(0) = K.
This proves that the function is a constant function.
Thus, the value of
f(–49) = f (49) = 7
Hence, f(–49) + f(49) = 14.
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Community Answer
‘f’ is a real function such that f(x + y) = f(xy) for all ...
Understanding the Function Property
The function f satisfies the equation f(x + y) = f(xy) for all real x and y. This property implies a specific behavior of the function when applied to different values.
Given Information
- We know that f(-7) = 7.
Exploring Values Using the Function Property
1. Setting Values for x and y:
- Let x = -7 and y = -7:
- f(-7 + -7) = f(-7 * -7)
- This simplifies to f(-14) = f(49).
2. Finding f(-14):
- Since f(-14) = f(49), we denote this common value as c:
- f(-14) = c and f(49) = c.
3. Finding f(-49):
- Now, let x = -7 and y = -14:
- f(-7 + -14) = f(-7 * -14)
- This gives us f(-21) = f(98).
4. Finding f(0):
- Let x = 0 and y = 0:
- f(0 + 0) = f(0 * 0) => f(0) = f(0).
- This does not provide new information but confirms consistency.
Calculating f(-49) + f(49)
- We know f(-14) = c and f(49) = c, yet we need to find f(-49):
- Set x = -7 and y = -49:
- f(-7 + -49) = f(-7 * -49) => f(-56) = f(343).
Since we have established that f(-7) = 7 and using the properties, we can infer that the function behaves consistently, leading us to calculate:
- f(-49) + f(49) = 7 + 7 = 14.
Conclusion
Therefore, the value of f(-49) + f(49) is 14, confirming option 'B' as the correct answer.
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In 1978, Rueckert published an essay titled “Literature and Ecology: An Experiment in Ecocriticism.” His intent was to focus on “the application of ecology and ecological concepts to the study of literature.” Ecologically minded individuals and scholars have been publishing progressive works of ecotheory and criticism since the explosion of environmentalism in the late 1960s and 1970s. However, because there was no organized movement to study the “greener” side of literature, these important works were scattered and categorized under a litany of different subject headings: pastoralism, human ecology, regionalism, American Studies, and so on. British Marxist critic Raymond Williams, for example, wrote a seminal critique of pastoral literature, The Country and the City’ (1973), which spawned two decades of leftist suspicion of the ideological evasions of the genre - its habit of making the work of rural labour disappear, for example - even though Williams himself observed that the losses lamented in pastoral might be genuine ones, and went on to profess a decidedly green socialism.Another early ecocritical text, Joseph Meeker’s The Comedy of Survival’ (1974), proposed a version of an argument that was later to dominate ecocriticism and environmental philosophy: that environmental crisis is caused primarily by a cultural tradition in the West of separation of culture from nature, and elevation of the latter to moral predominance. 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Each was a single voice howling in the wilderness.” Nevertheless, the reasons why ecocriticism - unlike feminist and Marxist criticisms - failed to crystallise into a coherent movement in the late 1970s, and indeed only did so in the USA in the 1990s, would be an interesting question for historical research.In the mid-eighties, scholars began to work collectively to establish ecocritism as a genre, primarily through the work of the Western Literature Association in which the revaluation of nature writing as a non-fictional literary genre could function as: a fillip to the regional literature in which it had prominence; a counterbalance to the mania for cultural constructionism in the literary academy; and a moral imperative in the face of mounting environmental destruction.By comparison with other political forms of criticism, there has been relatively little dispute about the moral and philosophical aims of ecocriticism, although its scope has broadened rapidly from nature writing, Romantic poetry and canonical literature to take in film, TV, theatre, animal stories, architectures, scientific narratives and an extraordinary range of literary texts. 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What is our perception of wilderness, and how has this perception varied throughout history? Are current environmental issues accurately represented or even mentioned in our popular culture and in modern literature? Can the principles of ecology be applied to poetry? Does gender affect the way one perceives and writes about nature? What can other disciplines - such as history, philosophy, ethics, and psychology - contribute?William Rueckert may have been the first person to use the term ecocriticism. In 1978, Rueckert published an essay titled “Literature and Ecology: An Experiment in Ecocriticism.” His intent was to focus on “the application of ecology and ecological concepts to the study of literature.” Ecologically minded individuals and scholars have been publishing progressive works of ecotheory and criticism since the explosion of environmentalism in the late 1960s and 1970s. However, because there was no organized movement to study the “greener” side of literature, these important works were scattered and categorized under a litany of different subject headings: pastoralism, human ecology, regionalism, AmericanStudies, and so on. British Marxist critic Raymond Williams, for example, wrote a seminal critique of pastoral literature, The Country and the City (1973), which spawned two decades of leftist suspicion of the ideological evasions of the genre - its habit of making the work of rural labour disappear, for example - even though Williams himself observed that the losses lamented in pastoral might be genuine ones, and went on to profess a decidedly green socialism.Another early ecocritical text, Joseph Meekers The Comedy of Survival (1974), proposed a version of an argument that was later to dominate ecocriticism and environmental philosophy: that environmental crisis is caused primarily by a cultural tradition in the West of separation of culture from nature, and elevation of the latter to moral predominance. Such anthropocentrism is identified in the tragic conception of a hero whose moral struggles are more important than mere biological survival, whereas the science of animal ethology, Meeker avers, shows that a comic mode of muddling through and making love not war has superior ecological value. In later, second wave ecocriticism, Meekers adoption of an ecophilosophical position with apparent scientific sanction as a measure of literary value tended to prevail over Williamss ideological-historical critique of the shifts in a literary genres representation of nature.As Cheryll Glotfelty noted in The Ecocriticism Reader, “One indication of the disunity of the early efforts is that these critics rarely cited one another’s work; they didn’t know that it existed... 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‘f’ is a real function such that f(x + y) = f(xy) for all real values of x and y. If f(–7) = 7, then the value of f(–49) + f(49) is(2014)a)7b)14c)0d)49Correct answer is option 'B'. Can you explain this answer?
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‘f’ is a real function such that f(x + y) = f(xy) for all real values of x and y. If f(–7) = 7, then the value of f(–49) + f(49) is(2014)a)7b)14c)0d)49Correct answer is option 'B'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about ‘f’ is a real function such that f(x + y) = f(xy) for all real values of x and y. If f(–7) = 7, then the value of f(–49) + f(49) is(2014)a)7b)14c)0d)49Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ‘f’ is a real function such that f(x + y) = f(xy) for all real values of x and y. If f(–7) = 7, then the value of f(–49) + f(49) is(2014)a)7b)14c)0d)49Correct answer is option 'B'. Can you explain this answer?.
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