Can someone tell me how to get the inverse?

A function is a little like a road map - we put in a starting point (x) and we can follow the map's directions (the formula) to arrive at an end destination ( f(x) ).

I'm gonna recalibrate our map first to make it easier to see where we're going:

The directions given by this map tell us this:

If our function shows us how to get to some destination, an inverse shows us the return trip. We can find the inverse of f(x) then by stepping through all of our directions in reverse:

If we swap the starting point and end destination - we'll start at x and call our end destination g(x) this time:

Presented a little cleaner:

d

step-by-step explanation:

given

y + 3 = - 4(x - 2) ← distribute the parenthesis

y + 3 = - 4x + 8 ( subtract 3 from both sides )

y = - 4x + 5 → d