Which of the following functions are continuous at x=1? f(x)=e^x-1 g(x)=ln(e^x-1) Choose 1 answer: (Choice A) f only (Choice B) g only (Choice C) Both f and g (Choice D) Neither f nor g

Check Continuity of f(x): Check if $f(x) = e^x - 1$ is continuous at $x=1$. Since $e^x - 1$ is an exponential function minus a constant, it is continuous everywhere.Check Continuity of g(x): Check if $g(x) = \ln(e^x - 1)$ is continuous at $x=1$. First, evaluate $e^x - 1$ at $x=1$: $e^1 - 1 = e - 1$. Since $e - 1 > 0$, $\ln(e - 1)$ is defined and continuous.Both Functions Continuous: Both $f(x)$ and $g(x)$ are continuous at $x=1$.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Which of the following functions are continuous at $x = 1$ ? $\newline$ $f(x) = e^x - 1$ $\newline$ $g(x) = \ln(e^x - 1)$ $\newline$ Choose $1$ answer: $\newline$ (Choice A) $f$ only $\newline$ (Choice B) $g$ only $\newline$ (Choice C) Both $f$ and $g$ $\newline$ (Choice D) Neither $f$ nor $g$

View step-by-step help

Home

Math Problems

Calculus

Find derivatives of sine and cosine functions

Full solution

Q. Which of the following functions are continuous at

x = 1

\newline

f(x) = e^x - 1

\newline

g(x) = \ln(e^x - 1)

\newline

Choose

1

answer:

\newline

(Choice A)

f

only

\newline

(Choice B)

g

only

\newline

(Choice C) Both

f

and

g

\newline

(Choice D) Neither

f

nor

g

Check Continuity of f(x): Check if $f(x) = e^x - 1$ is continuous at $x=1$ . $\newline$ Since $e^x - 1$ is an exponential function minus a constant, it is continuous everywhere.
Check Continuity of g(x): Check if $g(x) = \ln(e^x - 1)$ is continuous at $x=1$ . $\newline$ First, evaluate $e^x - 1$ at $x=1$ : $\newline$ $e^1 - 1 = e - 1$ . $\newline$ Since e - 1 > 0, $\ln(e - 1)$ is defined and continuous.
Both Functions Continuous: Both $f(x)$ and $g(x)$ are continuous at $x=1$ .