Question

Inverse Functions!
Use the theory of inverse functions to prove that f and g are inverse functions of eachother, and sketch the graph of f and g on the same coordinate plane.
f(x)=-x^2 + 3, x>=0 g(0)=sqrt(3-x), x<=3
I have no idea how I would start this D: Any help would be amazing! Thank you!!

Answer 1

Let's first check if they are inverse functions.
If g(x) is the inverse of f(x) then
\[f(g(x)=g(f(x)=x\]
Do you get this?

Answer 2

@Kilochan ???

Answer 3

Yes I did get that. But idk what to do after, so make a graph of two functions :O

Answer 4

Graph the equations as you would normally: g(x) and f(x) within the specified domain for x.

Answer 5

by "specidied domain" you mean x>=0 and x<=3? I've tried some graphing but they never came out as they were supposed to.

Answer 6

I will help.

Answer 7

So visually, from 0 to infinity, f(x) is graphed, and from -infinity to 3, g(x) is graphed. http://www.wolframalpha.com/input/?i=f%28x%29%3D-x%5E2+%2B+3%2C+g%28x%29%3Dsqrt%283-x%29

Answer 8

Hmmm. I did this exactly and the graph is coming out inverted. idk if I have a wrong mode on my calculator. it's in degree mode. My graphs are upside down. I put "-sqrt(3-x) and "-3-x^2" idk why they arent coming out the same. But your graphs are correct!

Answer 9

When I get rid of the negative signs, they come out right :O

Answer 10

@Kilochan i think you entered the wrong functions. You posted in the original question
"f(x)=-x^2 + 3, x>=0 g(0)=sqrt(3-x),"

then posted a moment ago
"-sqrt(3-x) and "-3-x^2"

Google can plot graphs too: https://www.google.com/search?q=sqrt(3-x)%2C+-x%5E2%2B3&oq=sqrt(3-x)%2C+-x%5E2%2B3&aqs=chrome.0.57j62l3.341&sourceid=chrome&ie=UTF-8

Answer 11

@agent0smith Yes, you are very right. I must have done some type of miscalculation. But now I see where I went wrong! Thank you everyone for your help!