Question

Diketahui fungsi f(x)=x+6 g(x)=2x²+4 dan h(x)=2x+5
Tentukan
a.(fogoh)(x)
b.(gofoh)(2)​

Answer 1

• [tex]f(x) = x + 6[/tex]
• [tex]g(x) = {2x}^{2} + 4[/tex]
• [tex]h(x) = 2x + 5[/tex]

Sehingga,

[tex]A. \: (fogoh)(x) = f(g(h(x)))[/tex]

• [tex](fogoh)(x) = f(g(2x + 5))[/tex]
• [tex](fogoh)(x) = f({2(2x + 5)}^{2} + 4)[/tex]
• [tex](fogoh)(x) = f(2({4x}^{2} + 20x + 25) + 4)[/tex]
• [tex](fogoh)(x) = f(({8x}^{2} + 40x + 50) + 4)[/tex]
• [tex](fogoh)(x) = f({8x}^{2} + 40x + 50 + 4)[/tex]
• [tex](fogoh)(x) = f({8x}^{2} + 40x + 54)[/tex]
• [tex](fogoh)(x) = ({8x}^{2} + 40x + 54) + 6[/tex]
• [tex](fogoh)(x) = {8x}^{2} + 40x + 54 + 6[/tex]
• [tex](fogoh)(x) = {8x}^{2} + 40x + 60[/tex]

[tex]B. \: (gofoh)(2) = g(f(h(2)))[/tex]

• [tex](gofoh)(2) = g(f(2(2) + 5))[/tex]
• [tex](gofoh)(2) = g(f(4 + 5))[/tex]
• [tex](gofoh)(2) = g(f(9))[/tex]
• [tex](gofoh)(2) = g(9 + 6)[/tex]
• [tex](gofoh)(2) = g(15)[/tex]
• [tex](gofoh)(2) = {2(15)}^{2} + 4[/tex]
• [tex](gofoh)(2) = 2(225) + 4[/tex]
• [tex](gofoh)(2) = 450 + 4[/tex]
• [tex](gofoh)(2) = 454[/tex]