Final answer:
To find the inverse function of f(x) = -4√x - 1, swap the x and y variables, isolate the square root term, square both sides, and simplify the equation. The inverse function is g(x) = (x + 1)²/16.
Step-by-step explanation:
To find the inverse function of f(x) = -4√x - 1, we need to switch the x and y variables and solve for y.
Start by replacing f(x) with y:
y = -4√x - 1
Swap the x and y variables:
x = -4√y - 1
Now solve for y by isolating the √y term:
x + 1 = -4√y
Divide both sides by -4 to solve for √y:
(√y) = (x + 1)/-4
Square both sides to get rid of the square root:
y = ((x + 1)/-4)²
Simplify the equation:
y = (x + 1)²/16
Therefore, the inverse function of f(x) = -4√x - 1 is g(x) = (x + 1)²/16.