Soalan 7:
Diberi f:x→
5x
mx−3
,x≠
3
2
dan g:x→3−4x. Cari
(a) nilai bagi m, [2 markah]
(b) gf-1(–2), [3 markah]
(c) fungsi h jika hg (x) = 12x + 5 [3 markah]Penyelesaian:
(a)
mx−3=0
m(
3
2
)−3=0
m=3×
2
3
=2
(b)
Katakan y=
5x
2x−3
2xy−3y=5x
2xy−5x=3y
x(
2y−5
)=3y
x=
3y
2y−5
f
−1
(
y
)=
3y
2y−5
f
−1
(
x
)=
3x
2x−5
f
−1
(
−2
)=
3(
−2
)
2(
−2
)−5
=
2
3
g
f
−1
(
−2
)=g(
2
3
)
=3−4(
2
3
)
=
1
3
(c)
hg (x) = 12x + 5
h [g(x)] = 12x + 5
h(3 – 4x) = 12x + 5
Katakan u= 3 – 4x
x=
3−u
4
h(
u
)=12(
3−u
4
)+5
h(
u
)=9−3u+5
h(
u
)=14−3u
h(
x
)=14−3x