Find the range of the function

1. Aug 17, 2010

thereddevils

1. The problem statement, all variables and given/known data

The function f is defined by

f(x) = sqrt(7-3x) , x<=1

= 3x^2-4x+3 , x>1

(1) Find the range of f

(2) if g(x)=sqrt(7-3x) , h(x)=3x^2-4x+3 in the case where f is continuous , find the composite function hg and state its domain and range.

(3) Determine the largest set for the domain and the corresponding range such that hg is one to one.

2. Relevant equations

3. The attempt at a solution

(1) Range=[2,infinity)

(2) hg(x)=24-9x-4sqrt(7-3x)

domain=(- inifinity , 7/3)

range = [3 , infinity)

(3) some hints on this.

2. Aug 17, 2010

vela

Staff Emeritus
Re: fucntions

You didn't get the correct range in part (2).