Question

Let f(x) = -5x + 1 and g(x) = -3x, for x = all real numbers

a. Write down f(2)
b. Find f-1(x).
c. Hence, find f-1(-4).

Answer 1

f(2) is found by plugging 2 into f(x), resulting in -9. To find the inverse function f^-1(x), we derived y = (x - 1) / -5. Subsequently, we found f^-1(-4) to be 1.

Step-by-step explanation:

To answer the student's question:

1. f(2) is simply replacing x with 2 in the function f(x) = -5x + 1. So, f(2) = -5(2) + 1 = -10 + 1 = -9.
2. To find f^-1(x), which is the inverse function of f(x), we have to swap x and y and solve for y.
3. Let y = -5x + 1, then x = -5y + 1.
4. Solving for y gives y = (x - 1) / -5, so f^-1(x) = (x - 1) / -5.
5. f^-1(-4) is found by substituting x with -4 in the inverse function we derived.
6. f^-1(-4) = (-4 - 1) / -5 = (-5) / -5 = 1.