SOLUTION: determine if g is the inverse of f. http://i.imgur.com/Rbv9p8V.png f(x)=1 - x^2,x≥0; g(x)=-√1 - x

Algebra ->  Inverses -> SOLUTION: determine if g is the inverse of f. http://i.imgur.com/Rbv9p8V.png f(x)=1 - x^2,x≥0; g(x)=-√1 - x       Log On


   

Question 939683: determine if g is the inverse of f.
http://i.imgur.com/Rbv9p8V.png
f(x)=1 - x^2,x≥0; g(x)=-√1 - x
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
to determine if g is the inverse of f, find the inverse of f first
f%28x%29=1-x%5E2 .........recall that f%28x%29=y
y=1-x%5E2 ...swap x and y
x=1-y%5E2 ....solve for y
x%2By%5E2=1-y%5E2%2By%5E2
y%5E2%2Bx=1
y%5E2=1-x
y=sqrt%281-x%29 or
f%5E-1%28x%29=sqrt%281-x%29
so, here we have two solutions: f%5E-1%28x%29=sqrt%281-x%29 and f%5E-1%28x%29=-sqrt%281-x%29

since g%28x%29=-sqrt%281+-x+%29, means g%28x%29 IS the inverse of f