Question

tolong dijawab lah, lagi butuh cepat ini​

Answer 1

Nomor 4

•› Invers fungsi

Misal: [tex]\sf{f(x)=y}[/tex]

[tex]\begin{aligned}\sf{y}&=\sf{\frac{2x+1}{x-2}}\\\sf{y(x-2)}&=\sf{2x+1}\\\sf{xy-2y}&=\sf{2x+1}\\\sf{xy-2x}&=\sf{2y+1}\\\sf{x(y-2)}&=\sf{2y+1}\\\sf{x}&=\sf{\frac{2y+1}{y-2}}\\\end{aligned}[/tex]

Maka: [tex]\sf{f^{-1}(x)=\dfrac{2x+1}{x-2}}[/tex]

•› Nilai a

[tex]\begin{aligned}\sf{f^{-1}(a)}&=\sf{7}\\\sf{\frac{2a+1}{a-2}}&=\sf{7}\\\sf{2a+1}&=\sf{7(a-2)}\\\sf{2a+1}&=\sf{7a-14}\\\sf{2a-7a}&=\sf{-14-1}\\\sf{-5a}&=\sf{-15}\\\sf{a}&=\sf{\frac{-15}{-5}}\\\sf{a}&=\sf{3}\end{aligned}[/tex]

  

Nomor 5

a. f(x) = x² - 2x + 1

[tex]\begin{aligned}\sf{y}&=\sf{x^2-2x+1}\\\sf{y}&=\sf{(x-1)^2}\\\sf{\pm\sqrt{y}}&=\sf{x-1}\\\sf{x}&=\sf{\pm\sqrt{y}+1}\end{aligned}[/tex]

∴ Maka: [tex]\sf{f^{-1}(x)=\pm\sqrt{y}+1}[/tex]

b. f(x) = x² - 4

[tex]\begin{aligned}\sf{y}&=\sf{x^2-4}\\\sf{x^2}&=\sf{y+4}\\\sf{x}&=\sf{\pm\sqrt{y+4}}\end{aligned}[/tex]

∴ Maka: [tex]\sf{f^{-1}(x)=\pm\sqrt{x+4}}[/tex]

c. f(x) = 2 + √(x + 2)

[tex]\begin{aligned}\sf{y}&=\sf{2+\sqrt{x+2}}\\\sf{y-2}&=\sf{\sqrt{x+2}}\\\sf{(y-2)^2}&=\sf{(\sqrt{x+2})^2}\\\sf{y^2-4y+4}&=\sf{x+2}\\\sf{x}&=\sf{y^2-4y+4-2}\\\sf{x}&=\sf{y^2-4y+2}\end{aligned}[/tex]

∴ Maka: [tex]\sf{f^{-1}(x)=x^2+4y+2}[/tex]