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

Analyze Function f(x): Analyze the first function f(x) = e^(x). The exponential function e^(x) is known to be continuous for all real numbers. There are no points of discontinuity since the function is well-defined for every real number x.Analyze Function g(x): Analyze the second function g(x) = sqrt(x). The square root function sqrt(x) is continuous for its domain. However, it is only defined for non-negative real numbers (x >= 0). Therefore, it is not continuous for all real numbers because it is not defined for negative values of x.Choose Correct Answer: Choose the correct answer based on the analysis of both functions. Since f(x) = e^(x) is continuous for all real numbers and g(x) = sqrt(x) is not, the correct answer is (A) f only.

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

f(x)=e^(x)

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

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

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Math Problems

Algebra 1

Domain and range of square root functions: equations

Full solution

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

\newline

f(x)=e^{x}

\newline

g(x)=\sqrt{x}

\newline

Choose

1

answer:

\newline

(A)

f

only

\newline

(B)

g

only

\newline

f

and

g

\newline

(D) Neither

f

nor

g

Analyze Function $f(x)$ : Analyze the first function $f(x) = e^{x}$ . The exponential function $e^{x}$ is known to be continuous for all real numbers. There are no points of discontinuity since the function is well-defined for every real number $x$ .
Analyze Function $g(x)$ : Analyze the second function $g(x) = \sqrt{x}$ . The square root function $\sqrt{x}$ is continuous for its domain. However, it is only defined for non-negative real numbers ( $x \geq 0$ ). Therefore, it is not continuous for all real numbers because it is not defined for negative values of $x$ .
Choose Correct Answer: Choose the correct answer based on the analysis of both functions. $\newline$ Since $f(x) = e^{x}$ is continuous for all real numbers and $g(x) = \sqrt{x}$ is not, the correct answer is (A) $f$ only.