SAT Exam > SAT Questions > If f(x) = x2and g(x) = cosx, which of the fol...
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If f(x) = x2 and g(x) = cosx, which of the following is true?
- a)f + g is even function
- b)f – g is an odd function
- c)f + g is not defined
- d)f + g is an odd function
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If f(x) = x2and g(x) = cosx, which of the following is true?a)f + g is...
if f(x) is an odd function
So, f(−x)=−f(x)
F(−x)=cos(f(−x))
=cos(−f(x))
=cos(f(x))
=F(x)
So cos(f(x)) is an even function
So, f(x) and g(x) is an even function
Most Upvoted Answer
If f(x) = x2and g(x) = cosx, which of the following is true?a)f + g is...
It's answer is a
I can't post images anymore
Put ( -x) in place of x... In both f(x) and g(x)
You will come to know that both give same answer
So addind them will also give same answer
And that is princple of even function
I can't post images anymore
Put ( -x) in place of x... In both f(x) and g(x)
You will come to know that both give same answer
So addind them will also give same answer
And that is princple of even function
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Community Answer
If f(x) = x2and g(x) = cosx, which of the following is true?a)f + g is...
Explanation:
The given functions are f(x) = x^2 and g(x) = cos(x).
Even Function:
An even function is defined as a function that satisfies the following property:
f(-x) = f(x) for all x in the domain of the function.
Odd Function:
An odd function is defined as a function that satisfies the following property:
f(-x) = -f(x) for all x in the domain of the function.
Analysis of f(x) = x^2:
To determine whether f(x) is an even or odd function, we need to check if it satisfies the properties mentioned above.
Even Function:
Let's substitute -x into f(x) = x^2:
f(-x) = (-x)^2
f(-x) = x^2
As we can see, f(-x) = f(x) for all x in the domain of the function. Therefore, f(x) = x^2 is an even function.
Analysis of g(x) = cos(x):
To determine whether g(x) is an even or odd function, we need to check if it satisfies the properties mentioned above.
Even Function:
Let's substitute -x into g(x) = cos(x):
g(-x) = cos(-x)
Cosine function is an even function, which means cos(-x) = cos(x) for all x in the domain of the function. Therefore, g(x) = cos(x) is also an even function.
Conclusion:
From our analysis, we can conclude that both f(x) = x^2 and g(x) = cos(x) are even functions. Thus, the correct answer is option 'A' - f g is an even function.
The given functions are f(x) = x^2 and g(x) = cos(x).
Even Function:
An even function is defined as a function that satisfies the following property:
f(-x) = f(x) for all x in the domain of the function.
Odd Function:
An odd function is defined as a function that satisfies the following property:
f(-x) = -f(x) for all x in the domain of the function.
Analysis of f(x) = x^2:
To determine whether f(x) is an even or odd function, we need to check if it satisfies the properties mentioned above.
Even Function:
Let's substitute -x into f(x) = x^2:
f(-x) = (-x)^2
f(-x) = x^2
As we can see, f(-x) = f(x) for all x in the domain of the function. Therefore, f(x) = x^2 is an even function.
Analysis of g(x) = cos(x):
To determine whether g(x) is an even or odd function, we need to check if it satisfies the properties mentioned above.
Even Function:
Let's substitute -x into g(x) = cos(x):
g(-x) = cos(-x)
Cosine function is an even function, which means cos(-x) = cos(x) for all x in the domain of the function. Therefore, g(x) = cos(x) is also an even function.
Conclusion:
From our analysis, we can conclude that both f(x) = x^2 and g(x) = cos(x) are even functions. Thus, the correct answer is option 'A' - f g is an even function.
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If f(x) = x2and g(x) = cosx, which of the following is true?a)f + g is even functionb)f g is an odd functionc)f + g is not definedd)f + g is an odd functionCorrect answer is option 'A'. Can you explain this answer?
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