Question

Which function below is the inverse of f(x) = x2 − 16?

Answer 1

Do you know what an inverse is?

Answer 2

The Opp Basically ..

Answer 3

Kind of. With an inverse, you replace x with y and solve.
So x=y^2+16
\[x=y^2+16\]
\[x-16=y^2\]
\[\sqrt{x-16}=\sqrt{y^2}\]
\[y=\sqrt{x-16}\]

Answer 4

thank you !!

Answer 5

i dont think this is correct ??

Answer 6

x squared over 16

±4square root of x

±square root of the quantity x plus 16

1 over quantity x squared minus 16

Answer 7

http://www.wolframalpha.com/input/?i=inverse+of+x^2%2B16&dataset=
I just Wolfram Alpha'd it and it's correct.

Answer 8

i have no idea what Wolfram Alpha is but okayy
( I dont see an answer like it

Answer 9

Wolfram Alpha is basically a website that can give you an answer to almost anything. But I think your teacher is wrong. Or you put in the wrong question.

Answer 10

its a worksheet i didnt know how to do

Answer 11

@iPwnBunnies
Did I do something wrong here or?

Answer 12

no im just not sure if your web site is correct but thank you anyway

Answer 13

I'm 99.9999% sure that my website is correct.

Answer 14

@jim_thompson5910
Am I wrong? .-.

Answer 15

no

Answer 16

Or @mathmale can you check this out since it looks like everyone else is afk?

Answer 17

f(x) = x^2 − 16 is the original function, not f(x) = x^2 + 16

Answer 18

also, remember that

\[\Large x^2 = k \implies x = \pm \sqrt{k}\]

Answer 19

even though technically the plus/minus doesn't make it a function (so they contradict themselves here)

Answer 20

Ah so yes, I was wrong. Your answer would be +/- sqrt(x+16).

Answer 21

what's frustrating is that it should be

\[\Large y = \sqrt{x+16}\]

assuming x > 0 in the original function. This is because they ask for an inverse FUNCTION.

However, the answer choice

\[\Large y = \pm \sqrt{x+16}\]

is NOT a function because of the plus/minus. So they are contradicting themselves.

Answer 22

Well regular functions have the vertical line test to check if it's a function, don't they have the horizontal line test for inverse functions?

Answer 23

yes if the function fails the horizontal line test, then it doesn't have an inverse

Answer 24

restricting the domain changes that though

Answer 25

so that's why trig functions (which are periodic and aren't one-to-one in nature) have inverse functions

Answer 26

Hmm. Doesn't that mean a parabola (say, x^2) wouldn't have have an inverse? Yet it does, sqrt (x)