CA Foundation Exam > CA Foundation Questions > If g(x) = 3 – x2 then g(x) isa)an odd f...
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If g(x) = 3 – x2 then g(x) is
- a)an odd function
- b)a periodic function
- c)an even function
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If g(x) = 3 – x2 then g(x) isa)an odd functionb)a periodic funct...
Explanation:
To determine whether a function is odd or even, we need to check its symmetry about the y-axis and x-axis, respectively.
Odd function:
A function is odd if it satisfies the following condition:
f(-x) = -f(x)
Even function:
A function is even if it satisfies the following condition:
f(-x) = f(x)
Now, let's apply these conditions to the given function g(x) = 3x^2.
Odd or Even?
To check whether g(x) is odd or even, we need to substitute -x in place of x and simplify the expression.
g(-x) = 3(-x)^2
g(-x) = 3x^2
Now, let's compare g(-x) with -g(x) and g(x).
-g(x) = -3x^2
g(x) = 3x^2
We can see that g(-x) is not equal to -g(x) or g(x), which means that g(x) is neither odd nor even.
Therefore, the correct answer is option 'D', none of these.
Conclusion:
The given function g(x) = 3x^2 is neither odd nor even, as it does not satisfy the conditions of symmetry about the y-axis or x-axis.
To determine whether a function is odd or even, we need to check its symmetry about the y-axis and x-axis, respectively.
Odd function:
A function is odd if it satisfies the following condition:
f(-x) = -f(x)
Even function:
A function is even if it satisfies the following condition:
f(-x) = f(x)
Now, let's apply these conditions to the given function g(x) = 3x^2.
Odd or Even?
To check whether g(x) is odd or even, we need to substitute -x in place of x and simplify the expression.
g(-x) = 3(-x)^2
g(-x) = 3x^2
Now, let's compare g(-x) with -g(x) and g(x).
-g(x) = -3x^2
g(x) = 3x^2
We can see that g(-x) is not equal to -g(x) or g(x), which means that g(x) is neither odd nor even.
Therefore, the correct answer is option 'D', none of these.
Conclusion:
The given function g(x) = 3x^2 is neither odd nor even, as it does not satisfy the conditions of symmetry about the y-axis or x-axis.
Community Answer
If g(x) = 3 – x2 then g(x) isa)an odd functionb)a periodic funct...
In place of X replace -x. 3-(-x)=3-x which is g(X) it even function
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If g(x) = 3 – x2 then g(x) isa)an odd functionb)a periodic functionc)an even functiond)none of theseCorrect answer is option 'C'. Can you explain this answer?
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