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Q. 1

Expert-verifiedFound in: Page 395

Book edition
6th

Author(s)
Sullivan

Pages
1200 pages

ISBN
9780321795465

The domain of the function $f\left(x\right)=\frac{x+1}{2x+1}$ is _______.

The domain of the function $f\left(x\right)=\frac{x+1}{2x+1}$ is $\left\{x|x\ne -\frac{1}{2}\right\}$.

We have:

$f\left(x\right)=\frac{x+1}{2x+1}$

The domain of the function is the set of input values for which the function is real and defined.

Find the undefined points by comparing the denominator to zero:

$2x+1=0\phantom{\rule{0ex}{0ex}}2x=-1\phantom{\rule{0ex}{0ex}}x=-\frac{1}{2}$

The function domain is $x<-\frac{1}{2}\mathrm{or}\hspace{0.17em}x>-\frac{1}{2}$.

Interval notation: $\left(-\infty \hspace{0.17em},\hspace{0.17em}-\frac{1}{2}\right)\cup \left(-\frac{1}{2},\hspace{0.17em}\infty \hspace{0.17em}\right)$

Set builder form: $\left\{x|x\ne -\frac{1}{2}\right\}$

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