For the real-valued functions f(x)=squareroot of 3x+21 and g(x)=x-2 , find the composition f(g)and specify its domain using interval notation.

(f(g))(x)=?
domain of f(g)=?

Question

For the real-valued functions f(x)=squareroot of 3x+21 and g(x)=x-2 , find the composition f(g)and specify its domain using interval notation.

(f(g))(x)=?
domain of f(g)=?

anonymous · Answer

$$f(x)=\sqrt{3x+21}$$
$$g(x)=x-2$$
$$f(g(x))=f(x-2)=\sqrt{3(x-2)+21}$$

anonymous · Answer

which of course simplifies to 
$$\sqrt{3x+15}$$

anonymous · Answer

domain 
$$3x+15\geq0$$
$$3x\geq-15$$
$$x\geq-3$$

anonymous · Answer

w8, its f times g (x)

anonymous · Answer

well then it would be different but you wrote 
$$f(g(x))$$ which is a composition, not a multiplication

anonymous · Answer

(f times g)   (x)

anonymous · Answer

$$fg$$ is not the same as $$f(g)$$

anonymous · Answer

you wrote 
$$f(g(x))$$ twice so i will be willing to bet that that is what it is

anonymous · Answer

btw i made am mistake.

$$3x\geq-15
$$
$$x\geq-5$$