Question

consider a function f:R-R f(x)=4x+3. show that f is inversible . Find the inverse



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Answer 1

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Answer 2

Explanation:

$\boxed{"A \:function\: f is\: said \:to\: be\: invertible,\: if\: it \:is \:bijective (one-one\: and \:onto). }\\Let \:x_{1}, x_{2}\in R \: such \: that \: f(x_{1}) = f(x_{2}) \\ \implies4x_{1} + \cancel{3} =4 x_{2} + \cancel{3 } \\ \ \implies \cancel{4}x_{1} = \cancel{4} x_{2} \\ \ \implies x_{1} = x_{2} \\ \therefore \: f \: is \:one - one \\ \\ let \: y \in \: R \\ take \: y = f(x) \\ then, \\ \: y = 4x + 3 \\ 4x = y - 3 \\ x = \frac{y - 3}{4} \in R \\ \therefore \: f \: is \: onto \\\\\\ since \: f \: is \: \: one - one \: and \: onto, \: it \: is \: bijective \\ \therefore \: it \: is \: invertible \\ f \: inverse, \: {f}^{ -1 } = \frac{x - 3}{4}$

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