Answer:
g(x) = (5x + 1)/2.
Explanation:
To find the inverse of the function f(x) = (2x-1)/5, we can follow these steps:
Step 1: Replace f(x) with y: y = (2x-1)/5
Step 2: Swap x and y: x = (2y-1)/5
Step 3: Solve the equation for y.
Multiply both sides of the equation by 5 to eliminate the fraction:
5x = 2y - 1
Add 1 to both sides of the equation:
5x + 1 = 2y
Divide both sides of the equation by 2:
(5x + 1)/2 = y
Therefore, the inverse of the function f(x) = (2x-1)/5 is given by g(x) = (5x + 1)/2.