SOLUTION: determine if g is the inverse of f. http://i.imgur.com/nCQxKGv.png f(x)=4 + x^2,x≥0; g(x)=√x - 4

Algebra ->  Inverses -> SOLUTION: determine if g is the inverse of f. http://i.imgur.com/nCQxKGv.png f(x)=4 + x^2,x≥0; g(x)=√x - 4       Log On


   

Question 939682: determine if g is the inverse of f.
http://i.imgur.com/nCQxKGv.png
f(x)=4 + x^2,x≥0; g(x)=√x - 4
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=4+%2B+x%5E2, x%3E=0; g%28x%29=sqrt%28x-4%29
find inverse:
f%28x%29=4+%2B+x%5E2.........f%28x%29=y
y=4+%2B+x%5E2..........swap x and y

x=4+%2B+y%5E2
x-4=y%5E2
y=sqrt%28x-4%29

f%5E-1%28x%29=sqrt%28x-4%29 for x%3E=0
so, g%28x%29=sqrt%28x-4%29 in inverse f%28x%29=4+%2B+x%5E2

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+4+%2B+x%5E2%2C+sqrt%28x-4%29%29+