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

Answer:

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

Step-by-step 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:

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