Example 3:
Given f: x → hx + k and f2 : x → 4x + 15.
(a) Find the values of h and of k.
(b) Take h > 0, find the values of x for which f (x2) = 7x
(a) Find the values of h and of k.
(b) Take h > 0, find the values of x for which f (x2) = 7x
Solution:
(a)
Step 1:
Find f2 (x)
Find f2 (x)
Given f (x) = hx + k
f2 (x) = ff (x) = f (hx + k)
= h (hx + k) + k
= h2x + hk + k
Step 2:
Compare with given f2 (x)
Compare with given f2 (x)
f2 (x) = 4x + 15
h2x + 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
or
x = 1
or
x = 1