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 ->  Polynomials-and-rational-expressions -> 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 1202758: 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(39620) About Me  (Show Source):
You can put this solution on YOUR website!
main coefficient negative three, so since is function of x, parabola with a maximum, vertical symmetry axis, ....
Vertex at (0,5).
Range is the real numbers less than or equal to 5.

f%28x%29=-3x%5E2%2B5
graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C-3x%5E2%2B5%29


Two different inverses.
-3y%5E2%2B5=x
-3y%5E2=x-5
y%5E2=-%28x-5%29%2F3
y%5E2=%285-x%29%2F3
y=0%2B-+sqrt%28%285-x%29%2F3%29
.
.
.
graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C-sqrt%28%285-x%29%2F3%29%29

OR

graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Csqrt%28%285-x%29%2F3%29%29
and identifying domains and ranges to each should be clear.