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Identify the inverse of the function f(x)=(2x-1)/5

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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.

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