[tex]\mathbf{Task.} ~ \mathrm{Which~function~is~the~inverse~for~the~function~} f(x) = 3x - 9?[/tex]
[tex]\mathrm{Let~us~express}~x~ \mathrm{from~the~formula~} f(x) = 3x - 9 \colon[/tex]
[tex]f(x) + 9 = 3x;[/tex]
[tex]\dfrac{f(x) + 9}{3} = x;[/tex]
[tex]\dfrac{f(x)}{3} + 3 = x.[/tex]
[tex]\mathrm{Let} ~x = g(x)~ \mathrm{and} ~f(x) = x.[/tex]
[tex]\mathrm{So,} ~g(x) = \dfrac{x}{3}+ 3~ \mathrm{is~inverse~function~for~} f(x) = 3x - 9.[/tex]
[tex]Answer \colon ~ g(x) = \dfrac{x}{3}+ 3. ~ \blacktriangle[/tex]
