Web Analytics

Verified Answer :

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:

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

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