Question

Find functions f and g so that h(x) = (f o g)(x)
h(x) = 10/square root of 7x+6

Answer 1

How do I solve this? Somebody please show me easy steps. I have an exam tomorrow and I need to understand!

Answer 2

you have a lot of choices here

Answer 3

i assume it is
\[f\circ g(x)=\frac{10}{\sqrt{7x+6}}\]

Answer 4

you could say \(g(x)=7x+6,f(x)=\frac{10}{\sqrt{x}}\) then
\[f(g(x))=f(7x+6)=\frac{10}{\sqrt{7x+6}}\]

Answer 5

you could say
\[g(x)=\sqrt{7x+6},f(x)=\frac{10}{x}\] then
\[f(g(x))=f(\sqrt{7x+6})=\frac{10}{\sqrt{7x+6}}\]

Answer 6

you could say
\[g(x)=\frac{1}{\sqrt{7x+6}},f(x)=10x\] then
\[f(g(x))=f(\frac{1}{\sqrt{7x+6}})=\frac{10}{\sqrt{7x+6}}\]

Answer 7

you can probably come up with more if you like
but there is no one right answer,there are several ways to do it