Question

2 Select the correct answer. What is the inverse of function ? F(x)=10/9x+11 A.f-1(x)=9x-99/10 B.f-1(x)=9/10x+11 C.f-1(x)=9x+11/10 D.f-1(x)=10x-110/9

Answer 1

Consider f(x)=y.

$\begin{gathered} f(x)=y \\ x=f^{-1}(y) \end{gathered}$

Simplify the equation f(x)=y to obtain the value of x in terms of y.

$\begin{gathered} f(x)=y \\ \frac{10}{9}x+11=y \\ \frac{10}{9}x=y-11 \\ 10x=9y-99 \\ x=\frac{9y-99}{10} \end{gathered}$

So inverse of function is,

$f^{-1}(x)=\frac{9y-99}{10}$

Correct nswer is A part.