Question

Find the inverse function of : f(x)=2x-6.f(x)=2x−6.

Answer 1

$FUNCTIONS \\ \\ \\ To \: find \: the \: inverse \: , \: replace \: \\ f(x) \: with \: y . \\ \\ \: f(x) = 2x - 6 \\ \: \: \: \: \: \: \: \: \: y \: = \: 2x - 6 \\ \\ \: \: Interchange \: the \: variables \\ \: \: \: \: \: \: \: \: \: x = 2y - 6 \\ \\ \: \: \: \: \: \: \: \: \: Solve \: for \: y \: \\ \: \: \: \: \: \: \: \: y \: \: = \: 3 + \frac{x}{2} \\ \\ {f}^{ - 1} (x) = 3 + \frac{x}{2 }$

Answer 2

$\displaystyle f(x) = 2x - 6 \iff y = 2x - 6 \implies x = 2y - 6 \implies x+ 6 = 2y \implies \\ \\ y = \frac{1}{2}x + 3 \implies \bf f^{-1}(x) = \frac{1}{2}x + 3$