Question

If f(x) = 2(x/3 + 5), find what f inverse is equal to

Options:
A. f inverse(x) = (3x - 10) / 2
B. f inverse(x) = (x - 5) / 2
C. f inverse(x) = (2x - 10) / 3
D. f inverse(x) = (x + 5) / 2

Answer 1

The inverse function of f(x) = 2(x/3 + 5) is found by swapping x and y and solving for y, which gives us the answer f inverse(x) = (3x - 10) / 2, corresponding to Option A.

Step-by-step explanation:

The student asked to find the inverse of the function f(x) = 2(x/3 + 5). To find the inverse function, we need to perform several steps. First, we substitute f(x) with y to make the equation easier to manipulate:

y = 2(x/3 + 5)

Next, we swap x and y to begin solving for the inverse:

x = 2(y/3 + 5)

Then, we solve for y by performing inverse operations in reverse order:

1. Divide both sides by 2: (x/2) = y/3 + 5
2. Subtract 5 from both sides: (x/2) - 5 = y/3
3. Multiply both sides by 3 to isolate y: 3((x/2) - 5) = y

The inverse function is therefore y = 3(x/2) - 15, which simplifies to y = (3x/2) - 15. Finally, we express the inverse function in terms of f-1(x):

f-1(x) = (3x - 10) / 2

So, the correct option for the inverse function is Option A.