1.6 Function, SPM Practice (Long Question)

Question 5:
In diagram below, the function g maps set P to set Q and the function h maps set Q to set R.

(a) in terms of x, the function
(i) which maps set Q to set P,
(ii) h(x).
(b) the value of x such that gh(x) = 8x + 1.

g( x )=3x+2 Let  g 1 ( x )=y g( y )=x 3y+2=x y= x2 3 g 1 ( x )= x+2 3

hg( x )=12x+5 h( 3x+2 )=12x+5 g( x )=3x+2 Let u=3x+2    x= u2 3 h( u )=12( u2 3 )+5    =4u8+5    =4u3 h( x )=4x3

gh( x )=g( 4x3 )  =3( 4x3 )+2  =12x9+2  =12x7 12x7=8x+1    4x=8  x=2

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