Question

1.jika di ketahui F(x) = x² - 5x dan g(x) =2x+3.

tentukan: a. (Fog) (X).

b. (gof) (x)

C. (fog) (-2)​

Answer 1

• [tex]f(x) = {x}^{2} - 5x[/tex]
• [tex]g(x) = 2x + 3[/tex]

Sehingga,

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

• [tex](fog)(x) = f(2x + 3)[/tex]
• [tex](fog)(x) = {(2x + 3)}^{2} - 5(2x + 3)[/tex]
• [tex](fog)(x) = ({4x}^{2} + 12x + 9) - (10x + 15)[/tex]
• [tex](fog)(x) = {4x}^{2} + 12x + 9 - 10x - 15[/tex]
• [tex](fog)(x) = {4x}^{2} + 12x - 10x + 9 - 15[/tex]
• [tex](fog)(x) = {4x}^{2} + 2x - 6[/tex]

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

• [tex](gof)(x) = g({x}^{2} - 5x)[/tex]
• [tex](gof)(x) = 2({x}^{2} - 5x) + 3[/tex]
• [tex](gof)(x) = ({2x}^{2} - 10x) + 3[/tex]
• [tex](gof)(x) = {2x}^{2} - 10x + 3[/tex]

[tex]C. \: (fog)( - 2) = f(g( - 2))[/tex]

• [tex](fog)( - 2) = f(2( - 2) + 3)[/tex]
• [tex](fog)( - 2) = f(( - 4) + 3)[/tex]
• [tex](fog)( - 2) = f( - 1)[/tex]
• [tex](fog)( - 2) = {( - 1)}^{2} - 5( - 1)[/tex]
• [tex](fog)( - 2) = 1 - ( - 5)[/tex]
• [tex](fog)( - 2) = 1 + 5[/tex]
• [tex](fog)( - 2) = 6[/tex]

Answer 2

Komposisi Fungsi

[tex] \begin{aligned} &\text{Diketahui} : & \!\!\!\! f(x) &=x^2 - 5x \\ && \!\!\!\! g(x) &= 2x+3 \end{aligned} [/tex]

[tex] \text{a. Tentukan } (f\circ g)(x). [/tex]

[tex]\quad \begin{aligned} (f\circ g)(x) &= f(g(x)) \\ &= f(2x+3) \\ &= (2x+3)^2-5(2x+3) \\ &= 4x^2+12x+9-10x-15 \\ &= 4x^2+2x-6 \end{aligned} [/tex]

[tex]\text{b. Tentukan } (g\circ f)(x). [/tex]

[tex] \quad \begin{aligned} (g\circ f)(x) &= g(f(x)) \\ &= g(x^2-5x) \\ &= 2(x^2-5x)+3 \\ &= 2x^2-10x+3 \end{aligned} [/tex]

[tex]\text{c. Tentukan } (f\circ g)(-2). [/tex]

[tex]\quad \begin{aligned} (f\circ g)(-2) &= 4(-2)^2+2(-2)-6 \\ &= 4(4)-4-6 \\ &= 16-10 \\ &= 6 \end{aligned} [/tex]

[tex] \colorbox{Orange}{\color{white}{\#ForTheGreaterGood}} [/tex]