SOLUTION: Consider f(x) = x^2 + 3, x < 0. What is the inverse of this function?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Consider f(x) = x^2 + 3, x < 0. What is the inverse of this function?      Log On


   

Question 1140475: Consider f(x) = x^2 + 3, x < 0. What is the inverse of this function?
Found 2 solutions by Boreal, MathLover1:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
y=x^2+3
x=y^2+3
x-3=y^2
y=+/- sqrt (x-3) inverse
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E2%2B3%2C-sqrt%28x-3%29%2Csqrt%28x-3%29%29

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=++x%5E2+%2B+3, x+%3C+0
Domain is negative real numbers.
Range is real numbers greater than 3.

the inverse of this function is:
Domain is real numbers greater than 3.
Range is negative real numbers.

find inverse with conditions above:
since f%28x%29+=y
y+=++x%5E2+%2B+3........swap x and y
x=++y%5E2+%2B+3
x-3=++y%5E2+

y+=-+sqrt%28x-3%29

=> f%5E-1%28x%29=+-+sqrt%28x-3%29