Which of the following functions are continuous for all real numbers? {:[g(x)=root(5)(x)],[h(x)=root(3)(x)]:} Choose 1 answer: (A) g only (B) h only (C) Both g and h (D) Neither g nor h

Analyzing g(x): Let's analyze the first function: g(x) = root(5)(x) This is the fifth root of x. The fifth root function is defined for all real numbers because we can take the fifth root of any real number, whether it is positive, negative, or zero.Analyzing h(x): Now let's analyze the second function: h(x) = root(3)(x) This is the cube root of x. The cube root function is also defined for all real numbers because we can take the cube root of any real number, just like the fifth root.Continuity of g(x) and h(x): Since both g(x) and h(x) are defined for all real numbers and do not have any points of discontinuity, we can conclude that both functions are continuous for all real numbers.Conclusion: Therefore, the correct answer is: (C) Both g and h

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Which of the following functions are continuous for all real numbers?

{:[g(x)=root(5)(x)],[h(x)=root(3)(x)]:}
Choose 1 answer:
(A)
g only
(B)
h only
(C) Both
g and
h
(D) Neither
g nor
h

Which of the following functions are continuous for all real numbers? $\newline$ $\begin{array}{l} g(x)=\sqrt[5]{x} \\ h(x)=\sqrt[3]{x} \end{array}$ $\newline$ Choose $1$ answer: $\newline$ (A) $g$ only $\newline$ (B) $h$ only $\newline$ (C) Both $g$ and $h$ $\newline$ (D) Neither $g$ nor $h$

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Algebra 2

Domain and range of absolute value functions: equations

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Q. Which of the following functions are continuous for all real numbers?

\newline

\begin{array}{l} g(x)=\sqrt[5]{x} \\ h(x)=\sqrt[3]{x} \end{array}

\newline

Choose

1

answer:

\newline

(A)

g

only

\newline

(B)

h

only

\newline

g

and

h

\newline

(D) Neither

g

nor

h

Analyzing $g(x)$ : Let's analyze the first function: $\newline$ $g(x) = \sqrt[5]{x}$ $\newline$ This is the fifth root of $x$ . The fifth root function is defined for all real numbers because we can take the fifth root of any real number, whether it is positive, negative, or zero.
Analyzing $h(x)$ : Now let's analyze the second function: $\newline$ $h(x) = \sqrt[3]{x}$ $\newline$ This is the cube root of $x$ . The cube root function is also defined for all real numbers because we can take the cube root of any real number, just like the fifth root.
Continuity of $g(x)$ and $h(x)$ : Since both $g(x)$ and $h(x)$ are defined for all real numbers and do not have any points of discontinuity, we can conclude that both functions are continuous for all real numbers.
Conclusion: Therefore, the correct answer is: $\newline$ $(C)$ Both $g$ and $h$