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Question

Let f(x)=xex1+x2+1 and g is either odd or even function. If fog is defined, then

A
fog is odd function
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B
fog is even function
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C
f(x) is even function
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D
f(x) is odd function
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Solution

The correct option is C f(x) is even function
f(x)=xex1+x2+1
f(x)=xex1x2+1
f(x)=xex1exx2+1
f(x)=2xexx+xex2(1ex)+1
f(x)=x(1ex)2x2(1ex)+1
f(x)=xex1+x2+1
f(x)=f(x)
f(x) is even function.

As we know composite of two functions (which are either odd or even) will be even if atleast one of them is even, so fog is even function.

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