Question

Nina belongs to a gym that charges $35 per month plus a $95 enrollment fee. She has found that the equation f(x) = 35x + 95 gives the total amount she has paid for x months. Find the inverse of this function.

Answer 1

The inverse of the function f(x) = 35x + 95 is f^-1(x) = (x - 95)/35.

Step-by-step explanation:

The inverse of a function can be found by swapping the dependent and independent variables. In this case, the function is f(x) = 35x + 95. To find the inverse, we replace f(x) with x and x with f(x):

x = 35f(x) + 95

Next, we solve for f(x) by isolating it on one side of the equation:

x - 95 = 35f(x)

To express f(x) on its own, we divide both sides of the equation by 35:

f(x) = (x - 95)/35

Therefore, the inverse of the function f(x) = 35x + 95 is f-1(x) = (x - 95)/35.