Function Expression :
\[f(x)=\sqrt{x^2-4x+3}+x \]Domain
\[\left]-\infty, 1\right] \cup \left[3, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 2 \]\[\lim_{x \overset{<}{\rightarrow1} }f(x) = 1 \]
\[\lim_{x \overset{>}{\rightarrow3} }f(x) = 3 \]
\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{x - 2}{\sqrt{x^{2} - 4 x + 3}} + 1 \]\[f^{\,\prime}(x)=\frac{x + \sqrt{x^{2} - 4 x + 3} - 2}{\sqrt{x^{2} - 4 x + 3}} \]
\[ \]
Integral
\[F(x) = \int \left(x + \sqrt{x^{2} - 4 x + 3}\right)\, dx \]Sign Table
Variation Table
Plot
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