1.6 Function, SPM Practice (Long Question)


Question 3:
Given that f : xhx + 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

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