Question

lf $f\left(x\right)$ and $g\left(x\right)$ are two functions such that $f\left(x\right)+g\left(x\right)=e^x$ and $f\left(x\right)-g\left(x\right)=e^{-x}$ then
I: $f\left(x\right)$ is an even function
II: $g\left(x\right)$ is an odd function
III: Both $f\left(x\right)$ and $g\left(x\right)$ are neither even nor odd.

• A. I and II are true
• B. only I is true
• C. only II is true
• D. only III is true

Answer 1

Answer: (A)

I and II are true

$f\left(x\right)=\frac{e^x+e^{-x}}{2};g\left(x\right)=\frac{e^x-e^{-x}}{2}$
$f(-x)=f\left(x\right);g(-x)=-g\left(x\right)$
Hence $f$ is even and $g$ is odd.