Question

If f(x)=1/9x-2, what is f–1(x)?

Answer 1

we are given

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

For finding inverse function , we do following steps

step-1:

Set f(x)=y

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

step-2:

Switch x and y

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

step-3:

now, we can solve for y

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

Multiply both sides by 9y-2

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

$x(9y-2)=1$

$9xy-2x=1$

Add both sides by 2x

$9xy-2x+2x=2x+1$

$9xy=2x+1$

now, we can divide both sides by 9x

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

so, we get inverse function as

$f^{-1}(x)=\frac{2x+1}{9x}$................Answer