Which of the following functions are continuous for all real numbers? g(x)=ln(x) f(x)=(1)/(x) Choose 1 answer: A) g only (B) f only (C) Both g and f (D) Neither g nor f

Question Prompt: Question prompt: Determine which of the given functions, g(x) = ln(x) and f(x) = 1/x, are continuous for all real numbers.Analyze g(x) = ln(x): Analyze the function g(x) = ln(x). The natural logarithm function ln(x) is defined only for x > 0. Therefore, g(x) is not continuous for all real numbers because it is not defined for x ≤ 0.Analyze f(x) = 1/x: Analyze the function f(x) = 1/x. The function 1/x is defined for all real numbers except x = 0, where it has a vertical asymptote. Therefore, f(x) is not continuous at x = 0 and thus not continuous for all real numbers.Conclusion: Since neither g(x) = ln(x) nor f(x) = 1/x is continuous for all real numbers, the correct answer is (D) Neither g nor f.

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Which of the following functions are continuous for all real numbers? $\newline$ $g(x)=\ln(x)$ $\newline$ $f(x)=\frac{1}{x}$ $\newline$ Choose $1$ answer: $\newline$ A) $g$ only $\newline$ (B) $f$ only $\newline$ (C) Both $g$ and $f$ $\newline$ (D) Neither $g$ nor $f$

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Intermediate Value Theorem

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

\newline

g(x)=\ln(x)

\newline

f(x)=\frac{1}{x}

\newline

Choose

1

answer:

\newline

g

only

\newline

(B)

f

only

\newline

g

and

f

\newline

(D) Neither

g

nor

f

Question Prompt: Question prompt: Determine which of the given functions, $g(x) = \ln(x)$ and $f(x) = \frac{1}{x}$ , are continuous for all real numbers.
Analyze $g(x) = \ln(x)$ : Analyze the function $g(x) = \ln(x)$ . The natural logarithm function $\ln(x)$ is defined only for x > 0. Therefore, $g(x)$ is not continuous for all real numbers because it is not defined for $x \leq 0$ .
Analyze $f(x) = \frac{1}{x}$ : Analyze the function $f(x) = \frac{1}{x}$ . The function $\frac{1}{x}$ is defined for all real numbers except $x = 0$ , where it has a vertical asymptote. Therefore, $f(x)$ is not continuous at $x = 0$ and thus not continuous for all real numbers.
Conclusion: Since neither $g(x) = \ln(x)$ nor $f(x) = \frac{1}{x}$ is continuous for all real numbers, the correct answer is (D) Neither $g$ nor $f$ .