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)=?

Answer 1

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

Answer 2

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

Answer 3

domain
\[3x+15\geq0\]
\[3x\geq-15\]
\[x\geq-3\]

Answer 4

w8, its f times g (x)

Answer 5

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

Answer 6

(f times g) (x)

Answer 7

\[fg\] is not the same as \[f(g)\]

Answer 8

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

Answer 9

btw i made am mistake.

\[3x\geq-15
\]
\[x\geq-5\]