Question

The number of solutions of the equation $a^{f\left(x\right)}+g\left(x\right)=0$, where $a>0$, $g\left(x\right)\ne 0$ and has minimum value $\frac{1}{2}$ is

• A. $1$
• B. $2$
• C. $0$
• D. $\infty$

Answer 1

The correct option is C

$0$

Explanation for correct option

Given $a^{f\left(x\right)}+g\left(x\right)=0$

where, $$\begin{gathered} g\left(x\right)>0 \\ a>0 \end{gathered}$$

For all $x\in \mathrm{ℝ},a^x>0$

As sum of positive number is always positive, so, sum of the given function will never be zero.

Therefore, no solution exist for the equation $a^{f\left(x\right)}+g\left(x\right)=0$

Hence, the correct option is $\left(\mathrm{C}\right)$.