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03 Jan 2016, 12:48
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D
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For which of the following functions is f(x) = f(−x) for all values of x ?
A. f(x) = x^3 + 3
B. f(x) = −x
C. f(x) = 2x + 3
D. f(x) = −x^2 + 2
E. f(x) = 5x − 4
A. f(x) = x^3 + 3
B. f(x) = −x
C. f(x) = 2x + 3
D. f(x) = −x^2 + 2
E. f(x) = 5x − 4
07 Jan 2016, 00:48
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Bunuel
Even Functions: A function is said to be even, if f(x) = f(-x)
Odd Functions: A function is said to be odd if f(x) = - f (-x)
However, the question can be solved without knowing the above definitions.
We need a function which remains the same after substituting x by -x
After looking at the options once, we identify that only Option D has an even power of x, rest all have odd powers, therefore replacing by -x will leave a negative sign.
Replacing x by -x in option D
f(-x) = - (-x)^2 + 2 = -x^2 + 2 + f(x)
Hence the correct answer is Option D
General Discussion
06 Jan 2016, 12:34
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Bunuel
f(x) = f(−x)
The above is a property of an even function .
f(x) = f^(n)
f(x) = f(−x) will hold when n is an even integer .
The only case when x is even is option D
Answer D
