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 To find the inverse, we first replace f(x) with y: y = 4x + 13x - 2 Then, we swap x and y: x = 4y + 13y - 2 Finally, we solve for y: y = (x + 2) / (4 + 13) = (x + 2) / 17 So, the inverse of f(x) = 4x + 13x - 2 is f^-1(x) = (x + 2) / 17

(b) f(x) = (x - 2)^3 Following the same steps: y = (x - 2)^3 Swap x and y: x = (y - 2)^3 Solve for y: y = cuberoot(x) + 2 So, the inverse of f(x) = (x - 2)^3 is f^-1(x) = cuberoot(x) + 2

(c) f(x) = √x + 5 Replace f(x) with y: y = √x + 5 Swap x and y: x = √y + 5 Solve for y: y = (x - 5)^2 So, the inverse of f(x) = √x + 5 is f^-1(x) = (x - 5)^2

(d) f(x) = 3x - 1 Replace f(x) with y: y = 3x - 1 Swap x and y: x = 3y - 1 Solve for y: y = (x + 1) / 3 So, the inverse of f(x) = 3x - 1 is f^-1(x) = (x + 1) / 3