Question

If h(x)=(f o g)(x) and h(x)=\root(4)(x+7), find g(x)=\root(4)(x+1)

Answer 1

if you're looking for f(x)

then

g(x) = sqrt(4x + 4)
h(x) = sqrt(4x + 28)

h(x)-g(x) = 24

meaning that sqrt(24) must be the constant of f(x)

f(x) = x(sqrt(24))

h(x) = f(g(x)) = (sqrt(24))(sqrt(4x+4)) = sqrt(4x+4+24) = sqrt(4x+28)

Answer 2

`f(x) = \sqrt[4]{x+6}`

Explanation:

Let
`h(x) = \sqrt[4]{x+7}` and
`g(x) = \sqrt[4]{x+1}`. By some algebraic handling:

`h(x) = \sqrt[4]{(x+1)+6}`

`h(x) = \sqrt[4]{(\sqrt[4]{x+1} )^(4)+6}`

But
`g(x) = \sqrt[4]{x+1}`. Therefore:

`f(x) = \sqrt[4]{x+6}`