Find the inverse of the following functions.(a) f (x) = 4x+13x−2(b) f (x) = (x − 2)3(c) f (x) = √x + 5(d) f (x) = 3x − 1

Sure, let's find the inverse of each function:

(a) f(x) = 4x + 13x - 2 First, let's simplify the function to f(x) = 17x - 2. To find the inverse, we replace f(x) with y, so we get y = 17x - 2. Next, we solve for x: x = (y + 2) / 17. Finally, we replace y with f^-1(x) to get the inverse function: f^-1(x) = (x + 2) / 17.

(b) f(x) = (x - 2)^3 We replace f(x) with y, so we get y = (x - 2)^3. Next, we solve for x: x = cuberoot(y) + 2. Finally, we replace y with f^-1(x) to get the inverse function: f^-1(x) = cuberoot(x) + 2.

(c) f(x) = √x + 5 We replace f(x) with y, so we get y = √x + 5. Next, we solve for x: x = (y - 5)^2. Finally, we replace y with f^-1(x) to get the inverse function: f^-1(x) = (x - 5)^2.

(d) f(x) = 3x - 1 We replace f(x) with y, so we get y = 3x - 1. Next, we solve for x: x = (y + 1) / 3. Finally, we replace y with f^-1(x) to get the inverse function: f^-1(x) = (x + 1) / 3.