Question

Find the inverse of the function (f(x) = -2log(1-4x) + 7).

a. (-(1)(2)logleft(1-(x)(2)right) + (7)(2))
b. (-(1)(4)logleft(1-(x)(2)right) + (7)(4))
c. (-(1)(2)logleft(1-(x)(4)right) + (7)(2))
d. (-(1)(4)logleft(1-(x)(4)right) + (7)(4))

Answer 1

To find the inverse of the function f(x) = -2log(1-4x) + 7, switch the x and y variables and solve for y. The inverse function is f^(-1)(x) = (10^((x-7) / -2) - 1) / 4.

Step-by-step explanation:

To find the inverse of the function f(x) = -2log(1-4x) + 7, we need to first switch the x and y variables and solve for y. The inverse function will be denoted as f-1(x).

1. Switch the x and y variables: x = -2log(1-4y) + 7
2. Solve for y: y = (10((x-7) / -2) - 1) / 4

Therefore, the inverse function is f-1(x) = (10((x-7) / -2) - 1) / 4.