Question

If f(x) = 9x + 1, find f–1 (f (3))

Answer 1

Answer:

The value of $f^{-1}(f(3))$ is 3.

Step-by-step 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,

$-9y=1-x$

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

Step 4 : replace y by $f^{-1}(x)$,

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

Now,

$f^{-1}(f(3))=f^{-1}(9\times 3+1)$   ( From equation (1) )

$=f^{-1}(28)$

$=\frac{28-1}{9}$     ( From equation (2) )

$=\frac{27}{9}$

$=3$

Answer 2

I hope this helps you