Question

How do I find the domain of (f*g)(x) for each f(x) and g(x):
f(x)=√x-2
g(x)= (1) / (4x)

and get x≤ 1/8?

Answer 1

\[f(x)=\sqrt{x-2}\] since you cannot take the square root of a negative number find the domain via
\[x-2\geq 0\] or
\[x\geq 2\]

Answer 2

is
\[g(x)=\frac{1}{4x}\]?

Answer 3

also, is it ]
\[f\times g(x)\] or
\[f\circ g(x)\]?

Answer 4

the second one. f∘g(x)

Answer 5

@satellite73

Answer 6

Basically its asking you for \[f(g(x))\] .

Answer 7

ooh ok that makes more sense

Answer 8

\[\large f\circ g(x)=f(g(x))=f(\frac{1}{4x})=\sqrt{\frac{1}{4x}-2}\]

Answer 9

since you cannot take the square root of a negative number, your job is to solve
\[\frac{1}{4x}-2\geq 0\]

Answer 10

you know how to do that?

Answer 11

yes

Answer 12

ok good
you should get
\[0<x\leq \frac{1}{8}\]

Answer 13

yup thats what i got! thanks!

Answer 14

yw