Explanation: To get the inverse of a function, we have to follow these steps: 1- replace f(x) with y 2- swap the x and y variables 3- solve for y 4- replace y with f⁻¹(x)
Applying this to the given as follows: f(x) = [tex] \frac{4x-3}{7} [/tex]
Step 1: replace f(x) with y: y = [tex] \frac{4x-3}{7} [/tex]
Step 2: swap the x and y variables: x = [tex] \frac{4y-3}{7} [/tex]
Step 3: solve for y: 7x = 4y - 3 4y = 7x - 3 y = [tex] \frac{7x-3}{4} [/tex]
Step 4: replace y with f⁻¹(x): f⁻¹(x) = [tex] \frac{7x-3}{4} [/tex]
