Question

diketahui f(x)=1/2x-1 dan g(x)=x²+1 tantukan a.(f⁰g)(x) b.(g⁰f)(x) dan c (f⁰g)(2) adalah​

Answer 1

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

[tex] \begin{align} (f\circ g)(x) &= f(g(x)) \\ &= f(x^2+1) \\ &= \dfrac{1}{2(x^2+1)-1} \\ &= \dfrac{1}{2x^2+1} \end{align} [/tex]

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

[tex] \begin{align} (g\circ f)(x) &= g(f(x)) \\ &= f(x^2+1) \\ &= \left(\dfrac{1}{2x-1}\right)^2+1 \\ &= \dfrac{1}{(2x-1)^2}+\dfrac{(2x-1)^2}{(2x-1)^2}\\ &= \dfrac{1+(2x-1)^2}{(2x-1)^2} \\ &= \dfrac{1+4x^2-4x+1}{4x^2-4x+1} \\ &= \dfrac{4x^2-4x+2}{4x^2-4x+1} \end{align} [/tex]

c. Tentukan [tex] (f\circ g)(2) [/tex]

[tex] \begin{align} (f\circ g)(2) &= \dfrac{1}{2(2)^2+1} \\ &= \dfrac{1}{2(4)+1} \\ &= \dfrac{1}{9}\end{align} [/tex]

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