Question

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

• A. $2$
• B. Infinitely many
• C. $0$
• D. $1$

Answer 1

The correct option is D $1$

Draw the graph of $y={\alpha }^{f\left(x\right)}$ and $y=–g\left(x\right)$ and observe the point of intersection of the graphs.