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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

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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Identify discrete and continuous random variables

Full solution

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

(A)

g

only

\newline

(B)

f

only

\newline

(C) Both

g

and

f

\newline

D Neither

g

nor

f

Determine Continuity: We need to determine the continuity of the functions $g(x) = \ln(x)$ and $f(x) = \frac{1}{x}$ for all real numbers.
Consider $g(x) = \ln(x)$ : Let's first consider $g(x) = \ln(x)$ . The natural logarithm function $\ln(x)$ is defined only for $x > 0$ . Therefore, it is not defined for $x \leq 0$ , which means it is not continuous for all real numbers.
Consider $f(x) = \frac{1}{x}$ : Now let's consider $f(x) = \frac{1}{x}$ . The function $\frac{1}{x}$ is defined for all real numbers except $x = 0$ , where it has a vertical asymptote. Therefore, it is not continuous at $x = 0$ .
Neither g nor f: 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 $f$ .

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\newline

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\newline

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