Find a formula h(x) and the domain of h?

Question

Find a formula h(x) and the domain of h. Enter using Interval Notation. 

 

f(x)= sqrt(3x-6)

 

g(x)= (2x^2)-7

 

A) h(x) = (f o g) (x)

 

h(x)= ?

 

domain= ?

 

 

 

B) h(x) = (g o f)(x)

 

h(x)= ?

 

domain= ?

 

 

C) h(x) = (f o f)(x)

h(x) = ?

domain= ?

 

 

D) h(x)= (g o g)(x)

h(x)= ?

domain= ?

 

 

 

 

Answer 1

h(x) = (f ο g)(x)

       = f(x)g(x)

       =(sqrt(3x-6))(2x²-7)

 

Domain:

 

There cannot be a negative number under the square root, therefore

 

3x-6≥0

3x≥6

x≥2

[2,∞)

 

Part a is the same as part b

 

Lets go to part c

 

function (f o f)(x) gives us a square of the square root.  This eliminates the square root so your domain is all real numbers.  (-∞,∞)

 

function (g o g)(x)  has domain (-∞,∞)