Math Problem Statement

Given the three functions below, which expression equals left parenthesis, c, circle, m, circle, p, right parenthesis, left parenthesis, x, right parenthesis(cmp)(x)?

c, left parenthesis, x, right parenthesis, equals, square root of, x, end square root, minus, 7, m, left parenthesis, x, right parenthesis, equals, x, cubed, p, left parenthesis, x, right parenthesis, equals, start fraction, 7, divided by, x, end fraction

c(x)=x​−7m(x)=x3p(x)=x7​

Answer

Multiple Choice Answers

left parenthesis, square root of, start fraction, 7, divided by, x, end fraction, end square root, minus, 7, right parenthesis, cubed(x7​​−7)3

start fraction, 7, divided by, left parenthesis, square root of, x, end square root, minus, 7, right parenthesis, cubed, end fraction(x​−7)37​

square root of, left parenthesis, start fraction, 7, divided by, x, end fraction, right parenthesis, cubed, end square root, minus, 7(x7​)3​−7

start fraction, 7, divided by, square root of, x, cubed, end square root, minus, 7, end fractionx3​−77​

Solution

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Math Problem Analysis

Mathematical Concepts

Composite Functions
Algebra
Radicals
Cubic Functions
Rational Expressions

Formulas

Composite function: (f ∘ g)(x) = f(g(x))
Square root function: √x
Cubic function: x³
Rational expression: 7/x

Theorems

Function composition
Properties of exponents and radicals

Suitable Grade Level

Grades 10-12