# HOW TO FIND INVERSE OF A FUNCTION

## About the topic "How to find inverse of a function"

"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.

## Steps involved in "How to find inverse of a function"

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

## Examples

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) = log₀(x)

Solution :

Step 1 :

Given function : h(x) = log₀(x)

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

Then, we will get  y = log₀(x) .

y = log₀(x) has been defined by "y" in terms of "x"

Step 2 :

Now we have to redefine y = log₀(x) by "x" in terms of "y"

y = log10(x) ===> 10y = x

or x = 10y

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

Step 3 :

In x = 10y replace "x" by h -1(x) and "y" by "x"

Hence inverse of h(x) is, h -1(x) = 10x

After having gone through the stuff given above, we hope that the students would have understood "How to find inverse of a function".

Apart from the stuff given above, if you want to know more about "How to find inverse of a 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

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

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

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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