Misalkan :
[tex]x + 3 = a[/tex]
[tex]x = a - 3[/tex]
Penyelesaian :
[tex]g(x) = 2(a - 3)[/tex]
[tex]g(x) = 2a - 6[/tex]
[tex]y = 2a - 6[/tex]
[tex]2a = y + 6[/tex]
[tex]a = \frac{y + 6}{2} [/tex]
[tex]g {}^{ - 1} (x) = \frac{x + 6}{2} [/tex]
[tex](gof)(x) = 4(a - 3) {}^{2} - 2[/tex]
[tex](gof)(x) = 4( {a}^{2} - 6a + 9) - 2[/tex]
[tex](gof)(x) = 4 {a}^{2} - 24a + 34[/tex]
[tex]g(f(x)) = 4 {a}^{2} - 24a + 34[/tex]
[tex]g(y) = 4( \frac{x + 6}{2} ) {}^{2} - 24( \frac{x + 6}{2} ) + 34[/tex]
[tex]g(y) = 4( \frac{ {x}^{2} + 12x + 36}{4} ) - 12(x + 6) + 34[/tex]
[tex]g(y) = {x}^{2} + 12x + 36 - 12x - 72 + 34[/tex]
[tex]g(y) = {x}^{2} - 2[/tex]
[tex]f(x) = {x}^{2} - 2[/tex]
[tex]y = {x}^{2} - 2[/tex]
[tex] {x}^{2} = y + 2[/tex]
[tex]x = \sqrt{y + 2} [/tex]
[tex]f {}^{ - 1} (x) = \sqrt{x + 2} [/tex]
[answer.2.content]
