SOLUTION: Given f(x)=-3x^2+5 a) Graph f and its inverse. b)Determine the equation of the inverse of f. c)State the domain and range of f and its inverse

Algebra ->  Graphs -> SOLUTION: Given f(x)=-3x^2+5 a) Graph f and its inverse. b)Determine the equation of the inverse of f. c)State the domain and range of f and its inverse      Log On


   

Question 936327: Given f(x)=-3x^2+5
a) Graph f and its inverse.
b)Determine the equation of the inverse of f.
c)State the domain and range of f and its inverse
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The domain of f is the range of its inverse.
The range of f is the domain of its inverse.

The vertex of f and the sign of leading coefficient tells you something about range for f.

The quick way to find the inverse of f is to switch function and x roles:
x=-3y%5E2%2B5
-3y%5E2=x-5
y%5E2=%28x-5%29%2F%28-3%29
y%5E2=-%28x-5%29%2F3
y=0%2B-+sqrt%28-%28x-5%29%2F3%29, the inverse of f.
Each branch is a separate function; when both branches are put together, that is not a function.


f(x)
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C-3x%5E2%2B5%29

The negative branch of inverse of f
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C-sqrt%28-%28x-5%29%2F3%29%29

The positive branch of inverse of f
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Csqrt%28-%28x-5%29%2F3%29%29