Function Expression :
\[f(x)=\frac{4x-5}{4x-4} \]Domain
\[\left]-\infty, 1\right[ \cup \left]1, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 1 \]\[\lim_{x \overset{<}{\rightarrow1} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow1} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 1 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{4 \cdot \left(4 x - 5\right)}{\left(4 x - 4\right)^{2}} + \frac{4}{4 x - 4} \]\[f^{\,\prime}(x)=\frac{1}{4 \left(x - 1\right)^{2}} \]
\[ \]
Integral
\[F(x) = x - \frac{\log{\left(x - 1 \right)}}{4} \]Sign Table
Variation Table
Plot
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