SOLUTION: f(x)=6-3x^2,if x<0 find the inverse of the one to one function f^-1(x)?

Algebra ->  Real-numbers -> SOLUTION: f(x)=6-3x^2,if x<0 find the inverse of the one to one function f^-1(x)?      Log On


   

Question 1135210: f(x)=6-3x^2,if x<0
find the inverse of the one to one function
f^-1(x)?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=6-3x%5E2,if x%3C0
find the inverse of the one to one function
f%5E-1%28x%29
since f+%28x%29=y, we have
y=6-3x%5E2.......swap x and y
x=6-3y%5E2........solve for y
3y%5E2=6-x
y%5E2=%286-x%29%2F3
y=sqrt%28%286-x%29%2F3%29
f%5E-1%28x%29=sqrt%28%286-x%29%2F3%29
so your inverse is: y=sqrt%28%286-x%29%2F3%29 or y=-sqrt%28%286-x%29%2F3%29
and it is one to one function