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

2 Answers

5 votes
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)
User Paul Trmbrth
by
8.8k points
7 votes

Answer:


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}

User Julxzs
by
8.4k points

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