Which is the inverse of the function f (x) = 1/4x + 1/2

f⁻¹(x) = 4x - 2

Step-by-step explanation:

To find the inverse of a function, switch the places of x and y (or f(x)).

f(x) = 1/4x + 1/2 → y = 1/4x + 1/2

Switch the variables.

x = 1/4y + 1/2

Now you want to convert the equation back into y = mx + b form.

x = 1/4y + 1/2

Subtract 1/2 from both sides.

x - 1/2 = 1/4y

Now, you want to isolate y further by dividing both sides by 1/4 (or multiplying by 4).

4(x - 1/2) = y

Distribute the 4.

4x - 2 = y → y = 4x - 2 → f⁻¹(x) = 4x - 2

This is the inverse of your given function.