SPM Practice (Long Question)

Question 3:
Given that f : x → hx + k and f² : x → 4x + 15.  
(a) Find the value of h and of k.
(b) Take the value of h > 0, find the values of x for which f (x² ) = 7x

Solution:
(a)
Given f (x) = hx + k
f² (x) = ff (x) = f (hx + k)
= h (hx + k) + k
= h² x + hk + k

f² (x) = 4x + 15
h² x + hk + k = 4x + 15
h² = 4
h = ± 2
when, h = 2
hk + k = 15
2k + k = 15
k = 5

When, h = –2
hk + k = 15
–2k + k = 15
k = –15

(b)
h > 0, h = 2, k = 5
Given f (x) = hx + k
f (x) = 2x + 5 f (x² ) = 7x
2 (x² ) + 5 = 7x
2x² – 7x + 5 = 0
(2x – 5)(x –1) = 0
2x – 5 = 0 or x –1= 0
x = 5/2 x = 1