Quiz Math Diketahui [tex] (g \circ f)(x) = 4x^2 + 16x + 9, \\ g(x) = x^2 - 7, f(10) = 24 [/tex]. Tentukan [tex] f^{-1}(x) [/tex]! (ingat konsep harga mutlak!)

jawab

g(x)  =  x² - 7

gof(x) = 4x² + 16x + 9
g {f(x)} = 4x² + 16x + 9
f²(x) - 7 =  4x² + 16x + 9
f² (x) = 4x² + 16x + 16 = (2x  + 4)²
f(x)= +_ (2x + 4)
f(10) = 24 --> f(x) = 2x + 4

f⁻¹ (2x +4)=  x
2x+ 4 = y
2x= y - 4
x = (y - 4)/ 2

f⁻¹ (x) = (x - 4)/2 
f⁻¹ (x) = ¹/₂ x - 2