Answer:
f⁻¹(x) = [tex] \frac{7x-3}{4} [/tex]
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]
Hope this helps :)
