Skorr

G(x)=x-1/2x+1, x≠- 12. Invers fungsi g(x) adalah g^-1(x)

Aljabar Matematika · SMA medium

Diketahui g(x)=x−12x+1, x≠−12g(x)=\dfrac{x-1}{2x+1},\ x\neq-\tfrac12. Invers fungsi g(x)g(x) adalah g−1(x)=....g^{-1}(x)=....

  1. A
    2x+1x−1, x≠1\dfrac{2x+1}{x-1},\ x\neq1
  2. B
    x+11−2x, x≠12\dfrac{x+1}{1-2x},\ x\neq\tfrac12
    ✓
  3. C
    x−21−x, x≠1\dfrac{x-2}{1-x},\ x\neq1
  4. D
    1−2xx+1, x≠−1\dfrac{1-2x}{x+1},\ x\neq-1
  5. E
    2x−1x+1, x≠−1\dfrac{2x-1}{x+1},\ x\neq-1

Kunci jawaban

B

Penjelasan singkat

y=x−12x+1⇒x=y+11−2yy=\dfrac{x-1}{2x+1}\Rightarrow x=\dfrac{y+1}{1-2y}, jadi g−1(x)=x+11−2xg^{-1}(x)=\dfrac{x+1}{1-2x}.

Misalkan y=x−12x+1y=\dfrac{x-1}{2x+1}. Kalikan silang: y(2x+1)=x−1⇒2xy+y=x−1y(2x+1)=x-1\Rightarrow 2xy+y=x-1.

2xy−x=−1−y⇒x(2y−1)=−(1+y)⇒x=y+11−2y2xy-x=-1-y\Rightarrow x(2y-1)=-(1+y)\Rightarrow x=\dfrac{y+1}{1-2y}.

Tukar peubah: g−1(x)=x+11−2x, x≠12g^{-1}(x)=\dfrac{x+1}{1-2x},\ x\neq\tfrac12. Jadi B.

⚡ Latihan Matematika SMA