Question

Composition of Functions and Inverses:Question 5Which answer represents the inverse of f(x)= 2x + 7? A. f^-1(x)= x-7/ 2B.f^-1(x)= -2x-7 C. f^-1(x)= x+7/2 D. f^-1(x)=2x-7

Answer 1

`f\mleft(x\mright)=2x+7`

to do this

Step 1

Let y=f(x)

swap positions x and y

`\begin{gathered} f(x)=2x+7 \\ y=2x+7 \\ \\ x=2y+7 \end{gathered}`

step 2

solve for y,

`\begin{gathered} x=2y+7 \\ x-7=2y \\ y=(x-7)/(2) \\ \\ so\text{ the answer is} \\ A)f^(-1)(x)=(x-7)/(2) \end{gathered}`