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)=((1)/(2))^x \end{gathered}`

Required:

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

Step-by-step explanation:

(5)

`\begin{gathered} f(-1)=3^(-1) \\ \\ =(1)/(3) \end{gathered}`

(6)

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

(7)

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

(8)

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

Final Answer:

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