Question

If f(-4) for f(x)=-2x+7 is 15, then what is f^-1 (15)?

Answer 1

To find f-1(15) for f(x)=-2x+7, we need to solve for x in terms of y and then substitute y with 15, resulting in f-1(15) being -4.

Step-by-step explanation:

If f(-4) for f(x)=-2x+7 is 15, then we can solve for the inverse function, f-1(15). First, let's affirm that if f(-4) = 15, it means we substitute x with -4 into the function:

f(-4) = -2(-4) + 7 = 8 + 7 = 15.

This checks out with the information given. To find the inverse function f-1(x) which gives us the value of x when f(x) is known, we would set f(x) equal to y and solve for x as follows:

y = -2x + 7
x = (y - 7) / -2.

Now we can find f-1(15) by replacing y with 15:

f-1(15) = (15 - 7) / -2 = 8 / -2 = -4.

Therefore, f-1(15) is -4.

Answer 2

let's recall that for a function f(x) that has an inverse function f⁻¹(x), the domain of f(x) corresponds to the range of f⁻¹(x), what the heck does that all mean?

well, it means that for any coordinate pairs (a , b) in f(x), there's a corresponding pair of (b , a) on f⁻¹(x).

we know in this case that f(-4) = 15, or namely that f(x) has a pair of (-4 , 15), well, that means that f⁻¹(x) has a swapped pair of (15 , -4).

the above means that f⁻¹(15) = -4.