Question

If f(x) = 9x + 1, find f–1 (f (3))

Answer 1

i hope this helps you

Answer 2

The value of
`f^(-1)(f(3))` is 3.

Explanation:

Here, the given function is,

`f(x)=9x+1-----(1)`

For finding
`f^(-1)(f(3))` we have to find out the inverse of f(x),

The steps are as follows,

Step 1 : Replace f(x) by y,

`y=9x+1`

Step 2 : Switch x and y,

`x=9y+1`

Step 3 : Isolate y in the left side,

`-9y=1-x`

`\implies y = (x-1)/(9)`

Step 4 : replace y by
`f^(-1)(x)`,

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

Now,

`f^(-1)(f(3))=f^(-1)(9* 3+1)` ( From equation (1) )

`=f^(-1)(28)`

`=(28-1)/(9)` ( From equation (2) )

`=(27)/(9)`

`=3`