For the real-valued functions f(x)=sqrt(5x+20) and g(x)=x-2 , find the composition f o g(x) and specify its domain using interval notation.

Question

For the real-valued functions f(x)=sqrt(5x+20)  and g(x)=x-2 , find the composition f o g(x) and specify its domain using interval notation.

hy123 · Answer

$$f(x)=\sqrt{5x+20}$$
g(x)= x-2

hy123 · Answer

Hey gane

hy123 · Answer

$$\sqrt{5(x-2)+20}$$

ganeshie8 · Answer

yep.. this is f(g(x))
we need to find its domain ?

hy123 · Answer

$$\sqrt{5x+10}$$?

hy123 · Answer

Do i need to factor or just leave it as it is? And domain would be (-infinity,-2) union (-2,+infinity)?

ganeshie8 · Answer

check again..

ganeshie8 · Answer

domain of a function is the set of all values we can supply as input..

ganeshie8 · Answer

since its a real valued function, 
5x+10 >= 0

hy123 · Answer

Oh wait... Uhh.... (-2,+infinity)?

ganeshie8 · Answer

its
[-2, infiniti)

-2 included... sqrt(0) is 0. its defined !!

hy123 · Answer

Arg -.-