What type of function is f(x) = frac{x - 2}{x | vedclass

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(A) Given the function $f(x) = \frac{x - 2}{x + 1}$,where $x 
eq -1$. To determine the nature of the function,we find its derivative $f'(x)$ using th

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Monotonically increasing

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(A) Given the function $f(x) = \frac{x - 2}{x + 1}$,where $x 
eq -1$. To determine the nature of the function,we find its derivative $f'(x)$ using the quotient rule: $f'(x) = \frac{(x + 1)(1) - (x - 2)(1)}{(x + 1)^2} = \frac{x + 1 - x + 2}{(x + 1)^2} = \frac{3}{(x + 1)^2}$. Since $(x + 1)^2 > 0$ for all $x \in R - \{-1\}$,it follows that $f'(x) = \frac{3}{(x + 1)^2} > 0$ for all $x \in R - \{-1\}$. Since the derivative is strictly positive for all $x$ in the domain,the function $f(x)$ is monotonically increasing.

What type of function is $f(x) = \frac{x - 2}{x + 1}$,where $x \neq -1$?

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