Find an equation for the inverse of the function. f (x) = 2x-3x/4

f⁻¹ (x) = (4x) / 5

Step-by-step explanation:

f (x) = 2x - 3x/4.

Assume y=f (x). Therefore:

y = 2x - 3x/4.

Make x the subject in the above equation.

y = (2x (4) - 3x) / 4.

y = 5x/4.

4y = 5x.

(4y) / 5 = x.

x = (4y) / 5.

Therefore:

f (y) = (4y) / 5.

Replace y with x.

f⁻¹ (x) = (4x) / 5.

Therefore, the inverse of f (x) = 2x - 3x/4 is f⁻¹ (x) = (4x) / 5!