Find the range of the function

[thereddevils]

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.

Homework Equations

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]

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

Try plotting hg(x). It'll help you see the answers for parts (2) and (3).

 

[thereddevils]

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

Try plotting hg(x). It'll help you see the answers for parts (2) and (3).

ok

got it!Thanks again Vela!