Question

Jika
f(x) = -x,
g(x + 3) = 2x + 5, dan
(h o g o f)^-1 (x) = (-x-5)/10.
Berapa nilai k agar h(k) = -10?

A. -4
B. -3
C. -2
D. 1
E. 2

(mohon jelaskan pakai cara, ya)

Answer 1

F(x) = -x

g(x+3)=2x+5
g(x) = 2(x-3)+5
=2x-6+5
=2x-1

(hogof)-¹(x) = (-x-5) / 10

hogof dalam bentuk invers maka inverskan lagi supaya inversnya hilang
jadi

y = (-x-5) / 10
10y = -x-5
x = -10y-5
(hogof)(x) = -10x-5


f(x) =-x dan g(x) =2x-1
(ho(gof) (x)
(gof)(x) = 2(-x) -1=-2x-1

h(-2x-1)(x) = -10x-5
misal
t = -2x-1
2x=-t-1
x=-t-1 / 2

h(x) = -10(-t-1 / 2) -5
=-5(-t-1)-5
=5t+5-5
=5t
h(x) =5x

h(k) =-10
5k=-10
k=-10/5
k=-2

solved