Question

Let f(x) = 10x + 12(a) Evaluate f(14)f(14)(b) Find the formula for the inverse of f(x):(c) Evaluate f^(-1)(- 9):

Answer 1

A.

T find f(14) we simply plug in the value in the formula:

`\begin{gathered} f(x)=10x+12 \\ \rightarrow f(14)=10(14)+12 \\ \Rightarrow f(14)=152 \end{gathered}`

B.

To find the inverse, we switch x and y, and then clear y :

`\begin{gathered} y=10x+12\rightarrow x=10y+12\rightarrow x-12=10y \\ \\ \rightarrow y=(x-12)/(10) \\ \\ \Rightarrow f^(-1)(x)=(x-12)/(10) \end{gathered}`

C.

We plug in -9 in the formula of the inverse of f(x):

`\begin{gathered} f^(-1)(x)=(x-12)/(10) \\ \\ \rightarrow f^(-1)(-9)=(-9-12)/(10) \\ \\ \Rightarrow f^(-1)(x)=-(21)/(10) \end{gathered}`