Answer:
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.
