Question

1. diketahui fungsi f(x)=2x-3 dan g(x)=x²+2x-3
tentukan!
a. fog (x)
b. gof (x)

bantu jawab guys!​

Answer 1

• [tex]f(x) = 2x - 3[/tex]
• [tex]g(x) = {x}^{2} + 2x - 3[/tex]

Sehingga,

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

• [tex](fog)(x) = f({x}^{2} + 2x - 3)[/tex]
• [tex](fog)(x) = 2({x}^{2} + 2x - 3) - 3[/tex]
• [tex](fog)(x) = ({2x}^{2} + 4x - 6) - 3[/tex]
• [tex](fog)(x) = {2x}^{2} + 4x - 6 - 3[/tex]
• [tex](fog)(x) = {2x}^{2} + 4x - 9[/tex]

[tex]B. \: (gof)(x) = g(f(x))[/tex]

• [tex](gof)(x) = g(2x - 3)[/tex]
• [tex](gof)(x) = {(2x - 3)}^{2} + 2(2x - 3) - 3[/tex]
• [tex](gof)(x) = ({4x}^{2} - 6x - 6x + 9) + 2(2x - 3) - 3[/tex]
• [tex](gof)(x) = ({4x}^{2} - 12x + 9) + (4x - 6) - 3[/tex]
• [tex](gof)(x) = {4x}^{2} - 12x + 9 + 4x - 6 - 3[/tex]
• [tex](gof)(x) = {4x}^{2} - 12x + 4x + 9 - 6 - 3[/tex]
• [tex](gof)(x) = {4x}^{2} - 8x + 0[/tex]
• [tex](gof)(x) = {4x}^{2} - 8x[/tex]