Question

Let $f$ be the exponential function and $g$ be the logarithmic function. Then, $(f+g)\left(1\right)$ :

• A. $0$
• B. $e$
• C. $\infty$
• D. None of these

Answer 1

The correct option is B $e$

We have,

$f:R\to R$ given by $f\left(x\right)=e^x$ and,

$g:R^{+}\to R$ given by $g\left(x\right)=lo{g}_{e}x$.

Since Domain(f) $\cap$ Domain (g) = $R\cap R^{+}=R^{+}$. Therefore,

$f+g:R^{+}\to R$ is given by

$(f+g)\left(x\right)=f\left(x\right)+g\left(x\right)=e^x+lo{g}_{e}x$ for all $x\in R^{+}$

Therefore, $(f+g)\left(1\right)=e^1+{\log }_{e}1=e+0=e$