Question

The number of solution of the equation $a^{f\left(x\right)}+g\left(x\right)=0,$ where $a>0,g\left(x\right)\ne 0$ and $g\left(x\right)$ has minimum value $\frac{1}{4}$, is

• A. one
• B. two
• C. infinitely many
• D. zero

Answer 1

The correct option is D zero

There are two terms in the question.
The first term is $a^{f\left(x\right)}$ where 'a' is positive, so this term will always be positive no matter what the value of $f\left(x\right)$ is.
Since its also mentioned that the minimum value of $g\left(x\right)$ is $\frac{1}{4}$, the sum of $2$ positive numbers cannot be zero.
Hence, there is no solution.