Question

If f(x) and f^(-1)(x) arejinverse functions of each other and f(x)=2x+5, what is f^(-1)(8)?

Answer 1

To find the value of f^(-1)(8), we first need to find the inverse function of f(x) = 2x + 5. After finding the inverse function, we substitute x = 8 to find f^(-1)(8) = 1.5.

Step-by-step explanation:

In this problem, we are given the function f(x) = 2x + 5 and we need to find f-1(8). To find the inverse function, we need to follow these steps:

1. Replace f(x) with y in the equation: y = 2x + 5.
2. Swap the x and y variables: x = 2y + 5.
3. Solve the equation for y. Subtract 5 from both sides and then divide by 2: y = (x - 5) / 2.
4. Replace y with f-1(x) to get the inverse function: f-1(x) = (x - 5) / 2.

Now we can find f-1(8) by plugging in x = 8 into the inverse function: f-1(8) = (8 - 5) / 2 = 3 / 2 = 1.5.