Question

I'm doing inverse functions.
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

I've done an equation like this but since it comes out as a fraction I'm not sure on what to do.

Answer 2

what is the inverse?

Answer 3

So y=f(x)
and f^{-1}(y)=x
So basically you find when 2x+5=8

Answer 4

Are if you want you can find the inverse first and then plug in directly into the inverse.

Answer 5

But solving 2x+5=8 will suffice.

Answer 6

f(x) = 2x + 5 OR
y = 2x + 5

Now, to find the inverse, we have to represent x in terms of y, and then switch the variables x and y. [This is a method to find the inverse of any function]

STEP 1 : Represent x in terms of y.

y = 2x + 5
y - 5 = 2x
x = (y-5)/2


STEP 2 : Switch the variables.

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

Now find f^{-1} (8).

:)

Answer 7

use @AkashdeepDeb method. That is appropriate.

Answer 8

So we're substituting x for 8? Sooooo 8 -5 = 3 divided by 2 equals 3/2

Answer 9

yes, you got it

Answer 10

2x+5=8 also gives you that.

Answer 11

it does but theoretically, you didn't state the inverse of f(x).

Answer 12

You're both right, but if you're trying to teach someone that doesn't quite understand it you would use the other method. Even though your method is simple.

Answer 13

In a test, you would be given points to show the approach of the inverse and the substitution.

Answer 14

Theoretically you do not need to find the actually inverse function to find the inverse at a certain number. :)