Question

-Given that f(x) = 6(x - 1). Choose the correct statement. A. f-1(12) = 3.5 B. f-1(3) = 1 c. f-16) = 3 D. f-1(9) = 2.5

Answer 1

Given that function is f(x) = 6(x - 1).

Let y = 6(x - 1). Replace x with y and then solve for y.

`\begin{gathered} x=6(y-1) \\ \Rightarrow x=6y-6 \\ \Rightarrow6y=x+6 \\ \Rightarrow y=(x+6)/(6) \end{gathered}`

Thus, f^-1(x) = (x + 6)/6.

`f^(-1)(12)=(12+6)/(6)=3`
`f^(-1)(3)=(3+6)/(6)=1.5`
`f^(-1)(6)=(6+6)/(6)=2`
`f^(-1)(9)=(9+6)/(6)=2.5`

Thus, option D is correct.