In math, an **inverse function** is a **function** that "reverses" the given **function**

For example, if f(x) is the given function, then f⁻¹ is the inverse of f(x).

"How to find inverse of a function?" is the question having had by almost all the students who study math in high schools.

Even though students can get this stuff on internet, they do not understand exactly what has been explained.

To make the students to understand "How to find inverse of any function", we have given step by step explanation.

**Step 1 :**

Let **f(x) = x + k** ("k" is a constant).

In the above function **f(x)** to be replaced by **"y"**.

Then, we will get **y = x + k**.

**y = x + k** has been defined by **"y"** in terms of **"x" **

**Step 2 :**

Now we have to redefine **y = x + k** by **"x"** in terms of **"y" **

Then we will get **x = y - k **

**Step 3 : **

In **x = y - k**, replace **"x"** by **f ⁻¹ (x)** and **"y"** by** "x"**.

Hence inverse of f(x) is, **f ⁻¹ (x) = x - k **

To have better understanding of the steps explained above, let us look at some examples.

**Problem 1 : **

Find the inverse of the function **f(x) = 2x + 3**

**Solution :**

**Step 1 :**

Given function : **f(x) = 2x + 3**

In the above function **f(x)** to be replaced by **"y"**.

Then, we will get **y = 2x + 3**.

**y = 2x + 3** has been defined by **"y"** in terms of **"x" **

**Step 2 :**

Now we have to redefine **y = 2x + 3** by **"x"** in terms of **"y" **

y = 2x + 3 ===> y - 3 = 2x

===> (y-3)/2 = x

====> **x = (y-3)/2**

Now, the function has been defined by "x" in terms of "y"

**Step 3 : **

In **x = (y - 3)/2**, replace **"x"** by **f ⁻¹ (x)** and **"y"** by** "x"**.

Hence inverse of f(x) is, **f ⁻¹ (x) = (x - 3)/2**

**Problem 2 : **

Find the inverse of the function **h(x) = log****₁****₀(x)**

**Solution :**

**Step 1 :**

Given function : **h(x) = log****₁****₀(x)**

In the above function **h(x)** to be replaced by **"y"**.

Then, we will get **y = **** log₁₀(x) **.

**y = **** log₁₀(x) **has been defined by

**Step 2 :**

Now we have to redefine **y = ****log₁₀(x) **by

Now, the function has been defined by "x" in terms of "y"

**Step 3 : **

Hence inverse of h(x) is,

After having gone through the stuff given above, we hope that the students would have understood "Inverse function".

Apart from the stuff given above, if you want to know more about "Inverse function", please click here

If you need any other stuff in math, please use our google custom search here.

**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**

**Sum of all three four digit numbers formed using 0, 1, 2, 3**

**Sum of all three four digit numbers formed using 1, 2, 5, 6**

HTML Comment Box is loading comments...