To find the inverse of a function, we switch out every x for a y and vice-versa.
Original: y = 4x + 8
Flipped: x = 4y + 8
Now, we solve for y again to put this equation into slope-intercept form.
x = 4y + 8
4y = x - 8
y = 1/4x - 2
h(x) = 1/4x - 2
Hope this helps!
