Respuesta :

lhannearaujo

The option D shows a function has a domain of all real numbers.

Which is the Domain of a Function?

The domain of a function is the set of input values for which the function is real and defined. In the other words, when you define the domain, you are indicating for which values x the function is real and defined.

  • Letter A - [tex]y=\left(x+2\right)^{^{\frac{1}{4}}\:}[/tex], as you have an even exponent, the results for y should be greater or equal than zero. Thus,

     [tex]\left(x+2\right)^{^{\frac{1}{4}}\:}=\sqrt[4]{x+2}[/tex]

      Therefore, the function domain is x  [tex]\geq[/tex]-2.

  • Letter B - [tex]y=-x^{\frac{1}{2}}^{\:}+5[/tex], as you have an even exponent, the results for y should be greater or equal than zero. Thus,

        [tex]-x^{\frac{1}{2}}^{\:}+5=-\sqrt{x} +5[/tex]

        x  [tex]\geq[/tex] 0

      Therefore, the function domain is x  [tex]\geq[/tex] 0.

  • Letter C - [tex]y=-2\left(3x\right)^{\frac{1}{6}}[/tex], as you have an even exponent, the results for y should be greater or equal than zero. Thus,

        [tex]-2\left(3x\right)^{\frac{1}{6}}=-2*\sqrt[6]{3x}[/tex]

          3x  [tex]\geq[/tex] 0

         x  [tex]\geq[/tex] 0

      Therefore, the function domain is x  [tex]\geq[/tex] 0.

  • Letter D - [tex]y=\left(2x\right)^{\frac{1}{3}}-7[/tex], as you have an odd exponent, the results for y has no undefined points nor domain constraints. Thus,

        [tex]\left(2x\right)^{\frac{1}{3}}-7=y=\sqrt[3]{2x} -7\\ \\[/tex]

         

      Therefore, the function domain is [tex]-\infty \: < x < \infty \:[/tex].

Learn more about  the domain here:

brainly.com/question/10197594  

#SPJ1