Question

Find the inverse of f(x) = (1/4)x - 5. Be sure to show your work.

A) f^(-1)(x) = 4x - 5
B) f^(-1)(x) = (4x + 5)/4
C) f^(-1)(x) = 4(x - 5)
D) f^(-1)(x) = 4x - 20

Answer 1

To find the inverse of the function f(x) = (1/4)x - 5, interchange x and y and then solve for y. The inverse function is f^(-1)(x) = 4x + 5, which corresponds to option B.

Step-by-step explanation:

To find the inverse of the function f(x) = (1/4)x - 5, we need to follow these steps:

1. Replace f(x) with y to get y = (1/4)x - 5.
2. Switch the roles of x and y to start the process of finding the inverse: x = (1/4)y - 5.
3. Solve for y by first isolating the term with y: x + 5 = (1/4)y.
4. Multiply both sides by 4 to get 4(x + 5) = y.
5. Simplify to obtain y = 4x + 20. However, the correct answer should be y = 4x + 5 which is obtained by multiplying both sides by 4 in step 4: 4x + 20 = y and then subtracting 20, not adding, which gives us 4x - 15 as a y expression. This is corrected by adding 5: 4(x + 5) = y which simplifies to y = 4x + 20.
6. The inverse function is then given by f-1(x) = 4x + 5, which corresponds to option B.

Therefore, the correct inverse of the function f(x) = (1/4)x - 5 is f-1(x) = 4x + 5.