Question

How do u do part b ? Help

Answer 1

If they are inverses, then when you have a composite function with the original and the inverse, it hits the y = x line. That is because an inverse is the original function reflected about the line y = x, and hence, the x and y-ordinates are interchanged.

Here's an example:
If $f(x) = 3x + 1$, find $f^{-1}(x)$ and prove that there is an inverse function.

Step 1) Interchange the x and y-values: $x = 3y + 1$
Step 2) Find an equation with y being the subject: $y = \frac{x - 1}{3}$

Now, that becomes your inverse function. So, if we find $f(f^{-1}(x))$ or $f^{-1}(f(x))$, then that should bring us back to x; ie there is a one-to-one function.

$f(f^{-1}(x)) = 3(\frac{x - 1}{3}) + 1$
$= x - 1 + 1$
$= x$

Thus, there is an inverse function at $f^{-1}(x) = \frac{x - 1}{3}$