Question

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

Answer 1

Answer:

B. 3/2

Step-by-step 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

Answer 2

Answer:

B. 3/2

Step-by-step 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: $f^{-1}(x)=\frac{x-5}{2}$

Plug in 8 for x:

$f^{-1}(x)=\frac{x-5}{2}$

$f^{-1}(8)=\frac{8-5}{2}=3/2$

The answer is thus B.

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