Question

Let f(x) =3 and g(x) = (1/2)^x, and evaluate the following: 5. f(-1)=6. f(-4)=7. f(2)+g(-2)=8. f(2)-g(-2)=

Answer 1

Given:

$\begin{gathered} f(x)=3^x \\ g(x)=(\frac{1}{2})^x \end{gathered}$

Required:

To find the value of f(-1), f(-4), f(2)+g(-2), f(2)-g(-2).

Explanation:

(5)

$\begin{gathered} f(-1)=3^{-1} \\ \\ =\frac{1}{3} \end{gathered}$

(6)

$\begin{gathered} f(-4)=3^{-4} \\ \\ =\frac{1}{3^4} \\ \\ =\frac{1}{81} \end{gathered}$

(7)

$\begin{gathered} f(2)+g(-2)=3^2+(\frac{1}{2})^{-2} \\ \\ =9+\frac{1}{2^{-2}} \\ \\ =9+2^2 \\ \\ =9+4 \\ \\ =13 \end{gathered}$

(8)

$\begin{gathered} f(2)-g(-2)=3^2-\frac{1}{2^{-2}} \\ \\ =9-2^2 \\ \\ =9-4 \\ \\ =5 \end{gathered}$

Final Answer:

$\begin{gathered} f(-1)=\frac{1}{3} \\ \\ f(-4)=\frac{1}{81} \\ \\ f(2)+g(-2)=13 \\ \\ f(2)-g(-2)=5 \end{gathered}$