**Composition of two functions examples :**

Here we are going to see how to find composition of two functions.

We follow the steps given below to find the composition of two functions f with g

**Step 1 :**

If f(x) = x and g(x) = 3x^{2}

fₒ g (x) = f [ g(x) ]

**Step 2 :**

In this step we have to apply the value 3x^{2 }instead of x in the function f (x).

f(3x^{2}) = 3x^{2}

**Step 3 :**

The answer that we got in step 2 represents the composition of two functions. If it is possible we have to simplify the answer in step 2.

That is,

fₒ g (x) = 3x^{2}

Let us look into some examples to understand the above concept.

**Example 1 :**

If f(x) = -4x + 2 and g(x) = √(x- 8) find fₒ g (x)

**Solution :**

Given : f(x) = -4x + 2 and g(x) = √(x- 8)

**Step 1 :**

fₒ g (x) = f [g(x)]

By applying the value of g(x) in the above step, we get

= f [ √(x- 8)]

**Step 2 :**

Now we have to apply x = √(x- 8) in the function of f (x).

= f(√(x- 8)) = -4√(x- 8) + 2

**Step 3 :**

We cannot simplify -4√(x- 8) + 2 here after.

Hence the value of fₒ g (x) is -4√(x- 8) + 2

Let us look into the next example on "Composition of two functions examples".

**Example 2 :**

If f(x) = -3x + 4 and g(x) = x^{2} find g ₒ f (x)

**Solution :**

Given : f(x) = -3x + 4 and g(x) = x^{2}

g ₒ f (x) = g [f(x)]

= g (-3x + 4)

Here x = -3x + 4. Now we are going to apply this value in the function g(x).

g(-3x + 4) = (-3x + 4)^{2}

We may expand this using algebraic identity

= (-3x)^{2} + 2 (-3x) (4) + 4^{2}

= 9x^{2} - 24x + 16

Hence the value of g ₒ f (x) is 9x^{2} - 24x + 16

**Example 3 :**

If f(x) = 2x - 5 and g(x) = x + 2 find f ₒ g (x)

**Solution :**

Given : f(x) = 2x - 5 and g(x) = x + 2

f ₒ g (x) = f [g(x)]

= f [x + 2]

In the function f(x), we have to apply x + 2 instead of x.

f(x + 2) = 2(x + 2) - 5

= 2x + 4 - 5

= 2x - 1

Hence the value of f ₒ g (x) is 2x - 1.

**Example 4 :**

If f(x) = -9x + 3 and g(x) = x^{4} find g ₒ f (x)

**Solution :**

Given : f(x) = -9x + 3 and g(x) = x^{4}

g ₒ f (x) = g [f(x)]

= g [-9x + 3]

In the function g(x), we have to apply -9x + 3 instead of x.

g(-9x + 3) = (-9x + 3)^{4}

Hence the value of g ₒ f (x) is (-9x + 3)^{4}

After having gone through the stuff given above, we hope that the students would have understood "Composition of two functions examples".

Apart from the stuff given above, if you want to know more about "Composition of two functions examples", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**