The function f: R-{1} rightarrow R-{4} define | vedclass

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(C) To check for one-one: Let $f(x_1) = f(x_2)$.$\frac{4x_1-3}{x_1-1} = \frac{4x_2-3}{x_2-1}$$(4x_1-3)(x_2-1) = (4x_2-3)(x_1-1)$$4x_1x_2 - 4x_1 - 3x_2

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One-one and onto

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(C) To check for one-one: Let $f(x_1) = f(x_2)$.$\frac{4x_1-3}{x_1-1} = \frac{4x_2-3}{x_2-1}$$(4x_1-3)(x_2-1) = (4x_2-3)(x_1-1)$$4x_1x_2 - 4x_1 - 3x_2 + 3 = 4x_1x_2 - 4x_2 - 3x_1 + 3$$-4x_1 - 3x_2 = -4x_2 - 3x_1$$x_1 = x_2$.Thus,the function is one-one.To check for onto: Let $y = \frac{4x-3}{x-1}$.$y(x-1) = 4x-3$$yx - y = 4x - 3$$yx - 4x = y - 3$$x(y-4) = y-3$$x = \frac{y-3}{y-4}$.For every $y \in R-\{4\}$,there exists an $x = \frac{y-3}{y-4} \in R-\{1\}$.Thus,the function is onto.Therefore,the function is one-one and onto.

The function $f: R-\{1\} \rightarrow R-\{4\}$ defined by $f(x) = \frac{4x-3}{x-1}$ for $x \in R-\{1\}$ is

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