Question

This one seems hard lol.

Question:
Let f(x) = 5x + 12. Find f^−1(x).

Answer Choices:
A) 12x + 5
B) 1 OVER 5x + 12 (Fraction)
C) 5 OVER x-12 (Fraction)
D) x-12 OVER 5 (Fraction)

Answer 1

@Maddy1251

Answer 2

Its f raised to the negative 1x power, right?

Answer 3

Yes.

Answer 4

Do you want to attempt it, and then see what you can come up with? I'm gonn try working it out :-)

Answer 5

Hmm, I'm already confused at the start with how I would being the process lol.

Answer 6

I brought more paper though to take notes. xD

Answer 7

At least you are prepared xD I had to go through my notes to figure this out. One second.

Answer 8

Okay lol, take your time. :)

Answer 9

Okay, so, we want to find the inverse of the function to solve for this. Big words, seems hard, actually really easy.

Answer 10

Lets start by setting f(x)=y, so that way it will be easy.

Answer 11

So we'd change the f(x) to y as in: y = 5x + 12 ??

Answer 12

y=5x+12. This is what it will look like. Yes.

Answer 13

Then, switch the x to a y in 5x+12, looking like x=5y+12.

Answer 14

Got that much?

Answer 15

Yup, I understand it so far! :)

Answer 16

Okay, now we want to solve for y , like we did for the other problems. :-)

Answer 17

(f^-1)(x)=(x-12)/5

Answer 18

How did you do that? Lol

Answer 19

x=5y+12
x-12=5y/5
(x-12)/5=x

Answer 20

We want to isolate the variable. I meant it equals y, not x. Force of habit. :P

Answer 21

Subtract 12 from both sides, that's the easiest way to start.

Answer 22

x=5y+12
-12 -12
Rule of math forever, what we do to one side, we do to the other.
x-12=5y

Answer 23

However, y is not by itself yet. For it to be isolated, or by itself, we then divide by 5, doing the inverse of what 5 is doing to y. Soooo, like I said, what you do to one side, we do to another.
(x-12)/5=5y/5

Answer 24

(x-12)/5=y, or f(x), since we changed y to f(x) for simple reasons.

Answer 25

Oh okay so since y=5 right now (5y) let's say it were 8y. Would you be this way: (x-12)/8=8y/8. So you're basically taking the y and dividing on each side then?

Answer 26

You're dividing by the number value, not the variable. But, you typed it correctly so I am assuming you know how to do it :-), We want 'y' alone, so we divided by 5, not y.

Answer 27

If we divided by 5, we would of had (x-12)/y=5

Answer 28

I mean *y*

Answer 29

Oh, xD Yes, that's what I meant, the 5 on each side, not the y. But I meant the number associated with the y variable. lol

Answer 30

Yep, because we were solving for 'y', and since subtracting 12 wasn't enough to get that little y variable alone, we divided by 5, because that was the opposite of what was being applied to y in this case. And you do it to each side, because that's that rule of math :)

Answer 31

5 had the attatchment to the y through multiplication, but 5 needed to go to the side where the 12 went, because y needed to be alone.

Answer 32

So, we divided by 5. inverse operations.

Answer 33

I see, I understand now. I thought it was going to be really tricky lol. So, what would we do next? I feel like x-12/5 is the answer, but are there any steps left?

Answer 34

Nope! There is nothing to be done, because the question asks to find f(x), which we did through all that lovely math. That is your final answer, since no substitution is needed, such as plugging in a variable such as 2.

Answer 35

Alright then! I'm glad we went over this one! I only have one left! :) I feel confident about all my answer because I am receiving help which makes me not so anxious haha. I'll tag you in the next one, once again, thank you. :)

Answer 36

Me too! Its good review for me, too :) Double winning. You got this.