fungsi invers dari [tex]f(x) = \frac{ {x }^{2} - 1}{ 2 - {x}^{2} } [/tex] plis bantuin..

jawab

f(x) = (x² -1) / (2 - x²)
y = (x² - 1)/(2 - x²)

x²  - 1 = y(2 - x²)
x² - 1 = 2y - yx²
x² + yx²= 2y  + 1
x²(1+ y)= (2y +1)
x² = (2y + 1)/(y+1)
x = √{(2y + 1)/(y+1)}

f⁻¹(x) = √ {(2x + 1)/(x+1)}
[tex] f^{-1}\, = \sqrt{ \frac{2x + 1}{x + 1} } [/tex]