Question

Determine the inverse of the function f(x) = 5/7x + 15/7.

Answer 1

The inverse of the function f(x) = (5/7)x + (15/7) is found by first swapping x and f(x), then solving for the new function, resulting in the inverse function f-1(x) = (7/5)x - (21/5).

Step-by-step explanation:

To determine the inverse of the function f(x) = (5/7)x + (15/7), we have to follow a series of steps. First, let's swap the x and f(x) variables to make it the inverse function. This gives us x = (5/7)f-1(x) + (15/7). Next, we'll solve for f-1(x) step by step:

1. Subtract (15/7) from both sides: x - (15/7) = (5/7)f-1(x).
2. Multiply both sides by (7/5) to isolate f-1(x): f-1(x) = (7/5)(x) - (21/5).

So, the inverse function is f-1(x) = (7/5)x - (21/5).