Question

what is the inverse of the function f(x)=1/9x+2

Answer 1

f(x) = 1/9x+2

-2 from both sides

f(x)-2 = 1/9x

*2 to both sides

9(f(x)-2) = x

replace 'f(x)' with 'x'

9(x-2) = f(x^-1)

simplify and reverse sides

f(x)^-1 = 9x-18

Answer 2

Answer:

$f^{-1}(x)=9x-18$

Step-by-step explanation:

we have

$f(x)=\frac{1}{9}x+2$

Let

$y=f(x)$

$y=\frac{1}{9}x+2$

Exchange variables x for y and y for x

$x=\frac{1}{9}y+2$

Isolate the variable y

$x-2=\frac{1}{9}y$

$y=9(x-2)$

$y=9x-18$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=9x-18$ -------> inverse function