Which of the following functions are continuous at x=2 ? {:[f(x)=root(4)(x-4)],[h(x)=log(x-4)]:} Choose 1 answer: (A) f only (B) h only (C) Both f and h (D) Neither f nor h

Determine Domain and Check: Determine the domain of f(x) and check if x=2 is within that domain. The function f(x) = root(4)(x-4) involves a fourth root. The fourth root is defined for all real numbers because we can take the fourth root of both positive and negative numbers. However, the expression inside the root, x-4, must be greater than or equal to zero for the function to be real-valued. Therefore, the domain of f(x) is x ≥ 4. Since 2 is not greater than or equal to 4, x=2 is not in the domain of f(x).Determine Domain and Check: Determine the domain of h(x) and check if x=2 is within that domain. The function h(x) = log(x-4) involves a logarithm. The argument of a logarithm must be positive. Therefore, the domain of h(x) is x > 4. Since 2 is not greater than 4, x=2 is not in the domain of h(x).Conclude Continuity: Conclude which functions are continuous at x=2 based on the domain analysis. Since neither f(x) nor h(x) have x=2 within their domains, neither function is continuous at x=2. Therefore, the correct answer is (D) Neither f nor h.

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Which of the following functions are continuous at
x=2 ?

{:[f(x)=root(4)(x-4)],[h(x)=log(x-4)]:}
Choose 1 answer:
(A)
f only
(B)
h only
(C) Both
f and
h
(D) Neither
f nor
h

Which of the following functions are continuous at $x=2$ ? $\newline$ $\begin{array}{l} f(x)=\sqrt[4]{x-4} \\ h(x)=\log (x-4) \end{array}$ $\newline$ Choose $1$ answer: $\newline$ (A) $f$ only $\newline$ (B) $h$ only $\newline$ (C) Both $f$ and $h$ $\newline$ (D) Neither $f$ nor $h$

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Math Problems

Algebra 2

Product property of logarithms

Full solution

Q. Which of the following functions are continuous at

x=2

\newline

\begin{array}{l} f(x)=\sqrt[4]{x-4} \\ h(x)=\log (x-4) \end{array}

\newline

Choose

1

answer:

\newline

(A)

f

only

\newline

(B)

h

only

\newline

f

and

h

\newline

(D) Neither

f

nor

h

Determine Domain and Check: Determine the domain of $f(x)$ and check if $x=2$ is within that domain. $\newline$ The function $f(x) = \sqrt[4]{x-4}$ involves a fourth root. The fourth root is defined for all real numbers because we can take the fourth root of both positive and negative numbers. However, the expression inside the root, $x-4$ , must be greater than or equal to zero for the function to be real-valued. Therefore, the domain of $f(x)$ is $x \geq 4$ . Since $2$ is not greater than or equal to $4$ , $x=2$ is not in the domain of $f(x)$ .
Determine Domain and Check: Determine the domain of $h(x)$ and check if $x=2$ is within that domain. $\newline$ The function $h(x) = \log(x-4)$ involves a logarithm. The argument of a logarithm must be positive. Therefore, the domain of $h(x)$ is x > 4. Since $2$ is not greater than $4$ , $x=2$ is not in the domain of $h(x)$ .
Conclude Continuity: Conclude which functions are continuous at $x=2$ based on the domain analysis. $\newline$ Since neither $f(x)$ nor $h(x)$ have $x=2$ within their domains, neither function is continuous at $x=2$ . Therefore, the correct answer is (D) Neither $f$ nor $h$ .