10th maths Exercise 1.5 - Question 1 Solution

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 ∫