Question

Soal tertera di gambar ​

Answer 1

Nomor 1

a.

[tex](fog)(x) = f(g(x))[/tex]

[tex](fog)(x) = 2(3x + 4) - 1[/tex]

[tex](fog)(x) = 6x + 8 - 1[/tex]

[tex](fog)(x) = 6x + 7[/tex]

b.

[tex](gof)(x) = g(f(x))[/tex]

[tex](gof)(x) = 3(2x - 1) + 4[/tex]

[tex](gof)(x) = 6x - 3 + 4[/tex]

[tex](gof)(x) = 6x + 1[/tex]

Nomor 2

[tex](fog)(x) = f(g(x))[/tex]

[tex](fog)(x) =(x + 4) {}^{2} - 1[/tex]

[tex](fog)( - 1) =( - 1 + 4) {}^{2} - 1[/tex]

[tex](fog)( - 1) =(3) {}^{2} - 1[/tex]

[tex](fog)( - 1) =9 - 1[/tex]

[tex](fog)( - 1) =8[/tex]

Nomor 3

a.

[tex](fogoh)(x) = f(g(h(x)))[/tex]

[tex](fogoh)(x) = f(g( {x}^{2} + 2x + 4))[/tex]

[tex](fogoh)(x) =f(( {x}^{2} + 2x + 4) - 4)[/tex]

[tex](fogoh)(x) =f( {x}^{2} + 2x)[/tex]

[tex](fogoh)(x) =2( {x}^{2} + 2x) + 1[/tex]

[tex](fogoh)(x) =2 {x}^{2} + 4x + 1[/tex]

b.

[tex](gohof)(x) = g(h(f(x)))[/tex]

[tex](gohof)(x) = g(h(2x + 1))[/tex]

[tex](gohof)(x) = g((2x + 1) {}^{2} + 2(2x + 1) + 4)[/tex]

[tex](gohof)(x) = g((4 {x}^{2} + 4x + 1) + 4x + 2 + 4)[/tex]

[tex](gohof)(x) = g(4 {x}^{2} + 8x + 7)[/tex]

[tex](gohof)(x) = (4 {x}^{2} + 8x + 7) - 4[/tex]

[tex](gohof)(x) = 4 {x}^{2} + 8x + 3[/tex]

Nomor 4

[tex](fohog)(x) = f(h(g(x)))[/tex]

[tex](fohog)(x) = f(h(2 {x}^{2} + 3x - 4 ))[/tex]

[tex](fohog)(x) =f((2 {x}^{2} + 3x - 4) + 2)[/tex]

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

[tex](fohog)(x) =3(2 {x}^{2} + 3x - 2) - 1[/tex]

[tex](fohog)(1) =3(2 {(1)}^{2} + 3(1) - 2) - 1[/tex]

[tex](fohog)(1) =3(2 + 3 - 2) - 1)[/tex]

[tex](fohog)(1) =3(3) - 1[/tex]

[tex](fohog)(1) =9 - 1[/tex]

[tex](fohog)(1) =8[/tex]

Nomor 5

[tex](fog)(x) = {x}^{2} + 2x - 4[/tex]

[tex]f(g(x)) = {x}^{2} + 2x - 4[/tex]

[tex]g(x) + 2 = {x}^{2} + 2x - 4[/tex]

[tex]g(x) = {x}^{2} + 2x - 4 - 2[/tex]

[tex]g(x) = {x }^{2} + 2x - 6[/tex]