Question

Find the inverse of the following function. Is the inverse a function?
y=(x-8)^2

I have an idea on how to do it I'm just not really sure and I'd like to know steps on how to do it.

Answer 1

Switch y and x in the equation and solve for y.

Answer 2

Step 1. x= (y-8) ^2 I have switched x and y

Answer 3

Step 2..x= (y-8)(y-8). Can you figure (y-8)(y-8) ?

Answer 4

So it would be y^2-16y+64? Then what? Solve for y?

Answer 5

I would switch the x and the y... then solve it so,

x=(y-8)^2

take the root of both sides now,

+-root(x) = y - 8

add 8 to boths

and y = +=-rootx - 8

this webside it .. nevermind

Answer 6

My bad... Ok we have the inverse as x=(y-8)^2. Now we have to isolate the y. So take the sqaure root of both sides gives you what?

Answer 7

The square root of both sides give you +-rootx=y-8? I'm not sure.

Answer 8

\[\sqrt{x}=y-8 You mean this?

Answer 9

\[\sqrt{x}=y-8\]

Answer 10

Yeah pretty much.

Answer 11

Now isolate y on one side of the equation and you have your inverse function. To solve any inverse just swap x and y in the original equation and solve for y.

Answer 12

Yeah, that's right. I had that on my homework and it was that.

Answer 13

Did you come up with an answer?

Answer 14

So in the end it would be y=+-√x-8?

Answer 15

\[y=\sqrt{x}+8\]

Answer 16

Add eight to both sides

Answer 17

Ohhh alright. Thanks. But I wouldn't be +-√x?

Answer 18

good observation @Josh422, if you take the square root of an expression you get a plus and a minus evaluation.

Answer 19

Oh wow thank you!

Answer 20

so what does that tell you? Is it a function?

Answer 21

Well wouldn't I have to graph it first to tell if it's one to one?

Answer 22

You're kind of right, a function and the graph of a function are basically the same thing. However, you can choose a more analytic approach. Maybe you have already had circles? and their definition? Circles clearly are no functions. Why? Because we give up on right uniqueness and therefore give up on functionality.

Answer 23

I'm fairly sure the answer is \[y=\sqrt{x} +8\]

Answer 24

Not sure where the +/- comes from.

Answer 25

Well yeah if it's the root then it should be plus or minus. Let's say "x" was 4. The square root of 4 can also be -2, as Negative two times Negative two would be 4.

Answer 26

You cannot have a negative number under a radical. You are thinking more in line with x^2 = 4..Where x can be 2 or -2.

Answer 27

@nelsonjedi, truth to be told, the question above lacks of description. It makes as good as no sense to talk about inverse functions when there is not even a domain and a codomain defined. Remember that you can only invert a function if it is bijective, meaning injective and surjective.

Hence the above function is neither at the moment. If we suppose it is bijective, then your answer is right and we can drop the plus or minus sign. But since this statement was not made, we cannot do such a thing and we would be better off by keeping the plus or minus sign.

Answer 28

Well thank you both for the help, I don't know how to give you badges to help you for helping me. But I'll have too go soon so thank you for the help. :). Also I've come to the conclusion that it's not a function. Would I be right?

Answer 29

Let me look

Answer 30

To determine if it is inverse you would take the Function f(x)= (x-8)^2 and use the Inverse function as your value for f(x) or x. If it equals x it is an inverse function. So we would get \[(\sqrt{x} + 8 - 8)^{2}\]

Answer 31

Subtract 8 from 8 and you left with \[\sqrt{x}^{2}\] Which equals x. So \[y=\sqrt{x} + 8 ....is.. an.. inverse.. function of.. y = (x+8)^{2}\]

Answer 32

Thank you.