Question

Find the function that corresponds to this inverse functionf(x)=3x+1/-5x-2, x ≠ -2/5

Answer 1

Answer::

`f^(-1)(x)=-(1+2x)/(3+5x),x\cancel{=}-(3)/(5)`

Explanation:

We want to find the function that corresponds to the inverse function:

`f(x)=(3x+1)/(-5x-2),x\cancel{=}-(2)/(5)`

To do this, we find the inverse of f(x).

In order to find the inverse of f(x), follow the steps below:

Step 1: Replace f(x) with y:

`y=(3x+1)/(-5x-2)`

Step 2: Swap x and y

`x=(3y+1)/(-5y-2)`

Step 3: Make y the subject of the equation:

Step 4: Replace y the inverse of f(x).

`f^(-1)(x)=(1+2x)/(-5x-3)=(1+2x)/(-(5x+3))=-(1+2x)/(3+5x)`

The function that corresponds to the given inverse function is:

`f^(-1)(x)=-(1+2x)/(3+5x),x\cancel{=}-(3)/(5)`