Final answer:
To find the inverse function of f(x) = 10x - 7, we solve for y by switching x and y to get x = 10y - 7 and then rearrange to y = (x + 7) / 10, resulting in f¹(x) = (x + 7) / 10.
Step-by-step explanation:
The student is asking for the inverse function of f(x) = 10x - 7. To find the inverse function, f¹(x), we need to switch the roles of x and y, and solve for y. Starting with y = 10x - 7, we swap x and y to get x = 10y - 7. Then we solve for y:
- Add 7 to both sides to get x + 7 = 10y.
- Divide both sides by 10 to solve for y, yielding y = (x + 7) / 10.
So, the inverse function is f¹(x) = (x + 7) / 10.