Question

If f(x)=2x+1/x-4, what is the value of f^-1(3)? A. 22/7 B. 19/11 C. 8/3 D. 13 E. 11

Answer 1

D

Explanation:

To find inverse function, we need to follow the steps:

1. Change f(x) to y

2. Interchange x and y

3. solve for new y

4. Change y to
`f^(-1)(x)`

Let's do this with the function given:

`f(x)=(2x+1)/(x-4)\\y=(2x+1)/(x-4)\\x=(2y+1)/(y-4)\\x(y-4)=2y+1\\xy-4x=2y+1\\xy-2y=4x+1\\y(x-2)=4x+1\\y=(4x+1)/(x-2)\\f^(-1)(x)=(4x+1)/(x-2)`

To find
`f^(-1)(3)`, we plug in 3 into the inverse equation:

`f^(-1)(x)=(4x+1)/(x-2)\\f^(-1)(3)=(4(3)+1)/((3)-2)\\f^(-1)(3)=(13)/(1)\\f^(-1)(3)=13`

D is the correct answer.