10th maths EXERCIsE 1.5 solution
10th maths Exercise 1.5 Question Number : 1
Using the functions ∫ and g given below,
find ∫ o g and g o∫. Check whether ∫ o g = g o ∫.
(i) ∫ (x) = x – 6, g(x) = x²
(ii) ∫ (x) = 2/x, g(x) = 2x² – 1
(iii) ∫ (x) = x+6/3, g(x) = 3 – x
(iv) f (x) = 3 + x, g(x) = x – 4
(v) ∫(x) = 4x²– 1, g(x) = 1 + x
Solution :
(i) ∫ (x) = x – 6, g(x) = x²
(∫ o g) (x) = ∫ (g(x))
= ∫ (x²)
= x² – 6
(g o ∫) (x) = g (∫ (x))
= g (x – 6)
= (x – 6)²
= x² – 12x + 36
∴ ∫ o g ≠ g o ∫
(ii) ∫ (x) = 2x, g (x) = 2x² – 1
(∫ o g) (x) = ∫ (g(x))
= f (2x² – 1)
= 2/2x²−1
(g o ∫) (x) = g (∫ (x))
=g(2/X)
=2(2/X)²-1
=8/X²-1
∴ ∫ o g ≠ g o ∫
