To find the inverse of the given function f(x) = (-2x - 3) / 4, we can follow these steps:
Step 1: Replace f(x) with y.
y = (-2x - 3) / 4
Step 2: Swap the x and y variables.
x = (-2y - 3) / 4
Step 3: Solve the equation for y.
Multiply both sides of the equation by 4 to eliminate the fraction:
4x = -2y - 3
Now, isolate y by moving -3 to the right side:
2y = -4x - 3
Divide both sides of the equation by 2:
y = (-4x - 3) / 2
Step 4: Replace y with the inverse notation f^(-1)(x).
f^(-1)(x) = (-4x - 3) / 2
Therefore, the inverse of the function f(x) = (-2x - 3) / 4 is f^(-1)(x) = (-4x - 3) / 2.