Function Composition: Find f and g for h(x) = √(x^6 + 7)

Math Problem Statement

like how do I do this question Find possible choices for outer and inner functions f and g such that the given function h equals

fcircle◦g.

h left parenthesis x right parenthesis equals StartRoot x Superscript 6 Baseline plus 7 EndRooth(x)=x6+7

Question content area bottom

Part 1

Choose the correct pair of functions below.

A.f left parenthesis x right parenthesis equals x cubed comma g left parenthesis x right parenthesis equals StartRoot x EndRoot minus 7

f left parenthesis x right parenthesis equals x cubed comma g left parenthesis x right parenthesis equals StartRoot x EndRoot minus 7f(x)=x3, g(x)=x−7

B.f left parenthesis x right parenthesis equals x Superscript 6 Baseline plus 7 comma g left parenthesis x right parenthesis equals StartRoot x EndRoot

f left parenthesis x right parenthesis equals x Superscript 6 Baseline plus 7 comma g left parenthesis x right parenthesis equals StartRoot x EndRootf(x)=x6+7, g(x)=x

C.f left parenthesis x right parenthesis equals StartRoot x EndRoot comma g left parenthesis x right parenthesis equals x Superscript 6 Baseline plus 7

f left parenthesis x right parenthesis equals StartRoot x EndRoot comma g left parenthesis x right parenthesis equals x Superscript 6 Baseline plus 7f(x)=x, g(x)=x6+7

D.f left parenthesis x right parenthesis equals StartRoot x EndRoot minus 7 comma g left parenthesis x right parenthesis equals x Superscript 6

f left parenthesis x right parenthesis equals StartRoot x EndRoot minus 7 comma g left parenthesis x right parenthesis equals x Superscript 6f(x)=x−7, g(x)=x6

Solution

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Math Problem Analysis

Mathematical Concepts

Function Composition
Radicals
Polynomials

Formulas

f(g(x)) = √(x^6 + 7)
g(x) = x^6 + 7
f(x) = √x

Theorems

Composition of Functions
Radical Function Theorem

Suitable Grade Level

Grades 10-12

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