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

Domain of h(x): To determine if h(x) = log(x) is continuous for all real numbers, we need to consider the domain of the logarithmic function. The logarithmic function is defined only for positive real numbers. Therefore, h(x) is not continuous for all real numbers because it is not defined for x ≤ 0.Cotangent function: Now, let's consider g(x) = cot(x). The cotangent function is the reciprocal of the tangent function. It is undefined whenever the tangent function is zero, which occurs at integer multiples of π. Therefore, g(x) is not continuous at these points and is not continuous for all real numbers.Conclusion: Since neither h(x) = log(x) nor g(x) = cot(x) is continuous for all real numbers, the correct answer is (D) Neither h nor g.

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

h(x)=log(x)

g(x)=cot(x)
Choose 1 answer:
(A)
h only
(B)
g only
(C) Both
h and
g
(D) Neither
h nor
g

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

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Math Problems

Algebra 2

Identify properties of logarithms

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

\newline

h(x)=\log (x)

\newline

g(x)=\cot (x)

\newline

Choose

1

answer:

\newline

(A)

h

only

\newline

(B)

g

only

\newline

h

and

g

\newline

(D) Neither

h

nor

g

Domain of $h(x)$ : To determine if $h(x) = \log(x)$ is continuous for all real numbers, we need to consider the domain of the logarithmic function. The logarithmic function is defined only for positive real numbers. Therefore, $h(x)$ is not continuous for all real numbers because it is not defined for $x \leq 0$ .
Cotangent function: Now, let's consider $g(x) = \cot(x)$ . The cotangent function is the reciprocal of the tangent function. It is undefined whenever the tangent function is zero, which occurs at integer multiples of $\pi$ . Therefore, $g(x)$ is not continuous at these points and is not continuous for all real numbers.
Conclusion: Since neither $h(x) = \log(x)$ nor $g(x) = \cot(x)$ is continuous for all real numbers, the correct answer is $(D)$ Neither $h$ nor $g$ .