Answer:
The inverse function of -5/(-9x + 2) is (-2x - 5) / (-9x).
Explanation:
To find the inverse function of -5/(-9x + 2), we need to swap the x and y variables and solve for y.
Step 1: Replace f(x) with y.
y = -5/(-9x + 2)
Step 2: Swap x and y.
x = -5/(-9y + 2)
Step 3: Solve for y.
Multiply both sides of the equation by (-9y + 2) to isolate y:
x(-9y + 2) = -5
Distribute x:
-9xy + 2x = -5
Move the terms with y to one side and the constant terms to the other side:
-9xy = -2x - 5
Divide both sides by -9x:
y = (-2x - 5) / (-9x)
Therefore, the inverse function of -5/(-9x + 2) is (-2x - 5) / (-9x).