Question

Let $f(x)$ be an odd function defined on $(-\infty ,\infty )$ and $g(x)$ be an even function defined on $(-\infty ,\infty )$.If $f(x)-g(x)=x^2+5x+7$, then $g(2)$ is equal to

• A. -13
• B. 9
• C. 7
• D. -11

Answer 1

Answer: (D)

We have $f(x)-g(x)=x^2+5x+7$....(1)
Replace $x\to -x$ in equation (1), we get
$f(-x)-g(-x)=x^2-5x+7$
$\Rightarrow -f(x)-g(x)=x^2-5x+7$
$\Rightarrow f(x)+g(x)=-x^2+5x-7$....(2)
$\therefore$ On solving (1) and (2),
we get $f(x)=5x$ and $g(x)=-x^2-7$
Hence $g(2)=-11$