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If h is the function given by ℎ(𝑥)=(𝑓∙𝑔)(𝑥)h(x)=(f∙g)(x) where f(x) =𝑥x​ and g(x) =(𝑥)3( x​ ) 3 , then h(x) =A.𝑥3x 3 B.𝑥x​ C.𝑥34x 43​ restricted to the domain x ≥≥ 0.D.𝑥2x 2 restricted to the domain x ≥≥ 0.E.𝑥2x 2 SUBMITarrow_backPREVIOUS

Question

If h is the function given by ℎ(𝑥)=(𝑓∙𝑔)(𝑥)h(x)=(f∙g)(x) where f(x) =𝑥x​ and g(x) =(𝑥)3( x​ ) 3 , then h(x) =A.𝑥3x 3 B.𝑥x​ C.𝑥34x 43​ restricted to the domain x ≥≥ 0.D.𝑥2x 2 restricted to the domain x ≥≥ 0.E.𝑥2x 2 SUBMITarrow_backPREVIOUS

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Solution

Para resolver la pregunta, sigamos los siguientes pasos:

  1. Identificar las funciones dadas:

    • f(x)=x f(x) = \sqrt{x}
    • g(x)=(x)3 g(x) = (\sqrt{x})^3

  2. Calcular g(x) g(x) :

    • g(x)=(x)3=x3/2 g(x) = (\sqrt{x})^3 = x^{3/2}

  3. Calcular h(x)=(f⋅g)(x) h(x) = (f \cdot g)(x) :

    • h(x)=f(x)⋅g(x) h(x) = f(x) \cdot g(x)
    • h(x)=x⋅x3/2 h(x) = \sqrt{x} \cdot x^{3/2}

  4. Simplificar h(x) h(x) :

    • h(x)=x1/2⋅x3/2 h(x) = x^{1/2} \cdot x^{3/2}
    • h(x)=x(1/2+3/2) h(x) = x^{(1/2 + 3/2)}
    • h(x)=x2 h(x) = x^2

  5. Determinar la restricción del dominio:

    • Dado que f(x)=x f(x) = \sqrt{x} y g(x)=(x)3 g(x) = (\sqrt{x})^3 , ambas funciones están definidas para x≥0 x \geq 0 .

Por lo tanto, la respuesta correcta es:

D. x2 x^2 restringido al dominio x≥0 x \geq 0 .

This problem has been solved

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