Question

If f(x)=1/9x-2, what is f–1(x)?

Answer 1

we are given

`f(x)=(1)/(9x-2)`

For finding inverse function , we do following steps

step-1:

Set f(x)=y

`y=(1)/(9x-2)`

step-2:

Switch x and y

`x=(1)/(9y-2)`

step-3:

now, we can solve for y

`x=(1)/(9y-2)`

Multiply both sides by 9y-2

`x* (9y-2)=(9y-2)* (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=(2x+1)/(9x)`

so, we get inverse function as

`f^(-1)(x)=(2x+1)/(9x)`................Answer