Question

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

A. -1
B. 3/2
C. 41/8
D. 23

Answer 1

B. 3/2

Explanation:

If f(x) and
`f^(-1)(x)` are inverse, that means that if we switch the x and y for f(x) and solve for y, we will get the inverse function.

Knowing that f(x) = 2x + 5, let's write this as y = 2x + 5 and switch the x and y:

x = 2y + 5

Now, solve for y:

x = 2y + 5

x - 5 = 2y

y = (x - 5)/2

That's the
`f^(-1)(x)` function:
`f^(-1)(x)=(x-5)/(2)`

Plug in 8 for x:

`f^(-1)(x)=(x-5)/(2)`

`f^(-1)(8)=(8-5)/(2)=3/2`

The answer is thus B.

~ an aesthetics lover

Answer 2

B. 3/2

Explanation:

When we have inverses, the input to one is the output of the other

f(x) = 2x+5

y = 2x+5

We want to find

f^ -1 (8)

So x becomes y and y becomes x in the inverse

That means we want y = 8 in the original function

8 = 2x+5

Subtract 5 from each side

8-5 = 2x+5-5

3 = 2x

Divide by 2

3/2 =x

This means the solution to

f^ -1 (8) = 3/2