Question

If $f\left(x\right)=e^{2x+2}$ then $f\left(a\right)f\left(b\right)$ is equal to

• A. $f\left(a+b\right)e^4$
• B. $f\left(a+b\right)e^2$
• C. $f\left(a+b\right)$
• D. None of these

Answer 1

The correct option is B $f\left(a+b\right)e^2$

$f\left(x\right)=e^{2x+2}$

$f\left(a\right)=e^{2a+2}$

$f\left(b\right)=e^{2b+2}$

$f(a+b)=e^{2(a+b)+2}$ ........$\left(1\right)$

Now $f\left(a\right)f\left(b\right)=e^{2a+2}{e}^{2b+2}$

$\Rightarrow f\left(a\right)f\left(b\right)=e^{2a+2+2b+2}=e^{2a+2b+2}{e}^2=f(a+b)e^2$ from $\left(1\right)$

Hence,$f\left(a\right)f\left(b\right)=f(a+b)e^2$