# Find the range of the function

## Homework Statement

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.

## 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.

vela
Staff Emeritus
Homework Helper

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

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