Question

for each function, find an equasion for the inverse. then use composition to verify that the equasion you wrote is the inverse.
g(x)=-6x+5

please explain how you got the answer

Answer 1

An inverse just undoes what the original function did, so you can get it by doing the opposite of what the original functtion did, in reverse order.

g(x) tells you: multiply by -6, then add 5.

Its inverse will tell you: subtract 5, then divide by -6.

Example: g(2) = 2*-6 + 5 = -7.
Inverse (call it h()):
h(-7) = (-7-5)/-6 = 2

so h(x) is going to look like (x-5)/-6.

Composition means finding h(g(x)); in other words write out g(x) in full instead of x and then apply h(x) to it, and if we're right, the whole mess should come back to be equal to x, where we started.

g(x)=-6x+5
h(g(x)) = ((-6x+5)-5)/-6

Does that get back to plain old x?