Question

Jika f(x)=px+q dan f(f(f(x)))=8x+21,maka p+q=
a.5
b.2
c.3
d.8
e.21

Answer 1

F(x) = px + q
f(f(f(x))) = 8x + 21
f(f(px + q)) = 8x + 21
f(p(px + q) + q) = 8x + 21
f(p²x + pq + q) = 8x + 21
p(p²x + pq + q) + q = 8x + 21
p³x + p²q + pq + q = 8x + 21
p³ = 8
p = ∛8 = 2

p²q + pq + q = 21
4q + 2q + q = 21
7q = 21
q = 3
p + q = 2 + 3 = 5

Answer 2

F(f(f(x))) = 8x + 21
f(f(px + q)) = 8x + 21
f( p( px + q) + q) = 8x + 21
f( p²x + pq + q) = 8x + 21
p( p²x + pq + q) + q = 8x + 21
p³x + p²q + pq + q = 8x + 21

p³x + p²q + pq + q = 8x + 21
brarti 
p³x = 8x
p³ = 8
p = 2

p³x + p²q + pq + q = 8x + 21
brarti 
p²q + pq + q =21      ----------  p diketahui samadengan 2
(2)²q + 2q + q =21
4q + 2q + q = 21
7q = 21
q = 3