Question

(i) If f (x) = x² – 1, g(x) = x – 2 find a, if gof(a) = 1. 

(ii) Find k, if f(k) = 2k – 1 and fof (k) = 5.

Answer 1

(i) f(x) = x² – 1, g(x) = x – 2 

Given gof(a) = 1 

gof(x) = g(f(x) 

= g(x² – 1) = x² – 1 – 2 

= x² – 3 

gof(a) ⇒ a² – 3 = 1 = + a² = 4 

a = ± 2

(ii) f(k) = 2k – 1

 fof(k) = 5 

f(f(k)m = f(2k – 1) = 5 

⇒ 2(2k – 1) – 1 = 5 

4 k – 2 – 1 = 5 ⇒ 4k = 8 

k = 2