Question

Consider ƒ : r → r given by f(x) = 4x+3, show that ƒ is invertible. find the inverse of ƒ.

Answer 1

$f(x) = 4x + 3 \\ for \: invertibility \\ let \\ f(x {}^{1} ) = f( {x}^{2} ) \\ {x}^{1} and \: {x}^{2} are \: notations \: not \: squares \\ \: or \: powers \\ 4 {x}^{1} + 3 = 4 {x}^{2} + 3 \\ subtract \: 3 \: from \: bot h \: sides \\ 4 {x}^{1} = 4 {x}^{2} \\ {x}^{1} = {x}^{2} \\ hence \: f(x) \: is \: invertible \\ ............ \\ ......... \\ for \: inverse \: \\ let \: \\ y = 4x + 3 \\ x = \frac{y - 3}{4} \\ replace \: y \: with \: x \\ {f}^{ - 1} (x) = \frac{x - 3}{4}$

since f(x) is linear function hence it's range is R.
and domain given in question is also R...
since domain =range.,
hence function is incredible.
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