Chapter 5 - Exponential and Logarithmic Functions - 5.3 One-to-One Functions; Inverse Functions - 5.3 Assess Your Understanding - Page 282: 100

(a) $240$, $(-5,240)$. (b) $-3$, $(-3,24)$. (c) $-1$.

(a) Given $F(x)=(\frac{1}{3})^x-3$, we have $F(-5)=(\frac{1}{3})^{-5}-3=240$ which gives a point $(-5,240)$. (b) For $F(x)=24$, we have $(\frac{1}{3})^x-3=24$ or $(\frac{1}{3})^x=27=(\frac{1}{3})^{-3}$, which gives $x=-3$ and a point $(-3,24)$. (c) Letting $F(x)=0$, we have $(\frac{1}{3})^x-3=0$ or $(\frac{1}{3})^x=3=(\frac{1}{3})^{-1}$, which gives $x=-1$.