The way I solve these is by first replacing f(x) with y. So now you have
y = 4x + 7/2
Next, switch the x and y around to get
x = 4y + 7/2
We then can solve for x by moving constants and coefficients.
x = 4y + 7/2
x - 7/2 = 4y
x/4 - 7/8 = y
Typically these equations are written in the form y = mx + b and inverse functions are notated as f'(x) so our final answer will be:
f'(x) = x/4 - 7/8