**Composition of functions examples :**

Here we are going to see some example problems on composition of functions.

Before going to see example problems, let us see what is composition function.

It is an operation being used to combine the given two functions.

Let f(x) and g(x) be the two functions.

The formula for composition of functions is given below in different forms.

**f∘g = f[g(x)]**

**f∘g(x) = f[g(x)]**

**f∘g(x²) = f[g(x²)]**

**Example 1 :**

Using f(x) = 4x + 3 and g(x) = x - 2, find: f(g(5))

**Solution :**

Before going to find the value of f(g(5)), first we have to find the value of f(g(x)).

f(x) = 4x + 3

g(x) = x - 2

f(g(x)) = 4 x - 8 + 3

= 4 x - 5

From this we can find the value of f(g(5)), for that we have to plug 5 instead of x in 4x - 5

f(g(x)) = 4 (5) - 5 ==> 20 - 5 ==> 15

Hence the value of f(g(5)) is 15.

**Example 2 :**

Using f(x) = 6 x² and g(x) = 14x + 4, find: g∘f(x)

**Solution :**

g∘f(x) = g [f(x)] = g [6 x²]

g(x) = 14x + 4

In the function g(x), we have to apply 6 x² instead of g(x)

g(x) = 14 (6 x²) + 4 ==> 84 x² + 4

**Example 3 :**

Using f(x) = 5x + 4 and g(x) = x - 3, find: f [g (6)]

**Solution :**

To find the value of f [g(6)], first we have to find the value of g(6)

here g(x) = x - 3

then g(6) = 6 - 3 ==> 3

f [g(6)] = f(3)

Now we have to apply 3 instead of x in the function f(x)

f(3) = 5 (3) + 4 ==> 15 + 4 ==> 19

Hence the value of f [g(6)] is 19.

**Example 4 :**

Using f(x) = 8x² and g(x) = 2x + 8, find: f∘g (x) and g∘f (x)

**Solution :**

f∘g (x) = f [g(x)]

= f [2x + 8]

To find the value of f [2x + 8], we have to apply 2x + 8 instead of x in the function f(x).

f [2x + 8] = 8(2x + 8)²

= 8 [4x² + 8² + 2(2x)(8)]

= 8 [4x² + 64 + 32x]

= 32x² + 512 + 256 x

= 32x² + 256 x + 512

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