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Question:
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Consider the following functions:
1- $f(x)=e^{x}$, where $x>0$
2- $g(x)=|x-3|$
Which of the above functions is/are continuous?
Options:
1- $f(x)=e^{x}$, where $x>0$
2- $g(x)=|x-3|$
Which of the above functions is/are continuous?
Solution:
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Verified Answer
The correct answer is:
Both 1 and 2
$\mathrm{f}(\mathrm{x})=\mathrm{e}^{\mathrm{x}}$, where $\mathrm{x}>0$
According to graph, Graph of $\mathrm{e}^{\mathrm{x}}$ is not breaking when $\mathrm{x}>0$ Therefore, graph is continuous at $\mathrm{x}>0$ Statement II $g(x)=|x-3|$
Graph of $|x-3|$ is not breaking but have sharp turn at $x$ $=3 .$
So, it is continuous
According to graph, Graph of $\mathrm{e}^{\mathrm{x}}$ is not breaking when $\mathrm{x}>0$ Therefore, graph is continuous at $\mathrm{x}>0$ Statement II $g(x)=|x-3|$
Graph of $|x-3|$ is not breaking but have sharp turn at $x$ $=3 .$
So, it is continuous
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