**Finding the Missing Value in Composition of Two Functions :**

Here we are going to see, how to find the missing value in composition of two functions.

**Question 1 :**

Find a number b such that f ◦ g = g ◦ f , where

f(x) = 2x + b and g(x) = 3x + 4.

**Solution :**

L.H.S

f ◦ g (x) = f [g(x)]

= f(3x + 4)

= 2(3x + 4) + b

= 6x + 8 + b ------(1)

R.H.S :

g ◦ f (x) = g [f(x)]

= g(2x + b)

= 3(2x + b) + 4

= 6x + 3b + 4 ------(2)

(1) = (2)

6x + 8 + b = 6x + 3b + 4

b - 3b = 4 - 8

-2b = -4

b = 2

Hence the value of b is 2.

**Question 2 :**

Find a number c such that f ◦ g = g ◦ f , where

f(x) = 5x − 2 and g(x) = cx − 3.

**Solution :**

L.H.S

f ◦ g (x) = f [g(x)]

= f(cx - 3)

= 5(cx - 3) - 2

= 5cx - 15 - 2

= 5cx - 17 ------(1)

R.H.S :

g ◦ f (x) = g [f(x)]

= g(5x - 2)

= c(5x - 2) - 3

= 5cx - 2c - 3 ------(2)

(1) = (2)

5cx - 17 = 5cx - 2c - 3

2c = -3 + 17

2c = 14

c = 14/2 = 7

c = 7

Hence the value of c is 7.

After having gone through the stuff given above, we hope that the students would have understood "Finding the Missing Value in Composition of Two Functions".

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