Question

How to find Inverse of f(x) = 2x + 3/4 ?

Answer 1

switch your x and y then sove for "x" like this:

y = 2x + (3/4) switch em

x = 2y + (3/4) ... now solve for "y"

x - (3/4) = 2y

x/2 - 3/8 = y

Answer 2

I always like the nest approach:
\[f(f^{-1}(x)) = x \text{, by the definition of the inverse}\]
\[\implies 2f^{-1}(x) + 3/4 = x\]
\[\implies 2f^{-1}(x) = x-3/4\]
\[\implies f^{-1}(x) = x/2-3/8\]