Inverse Functions with Fractions

Introduction to inverse functions with fractions:

Inverse functions:

In mathematics, if ƒ is a function from a set A to a set B, then an inverse function for ƒ is a function from B to A, with the property that a round trip (a composition) from A to B to A (or from B to A to B) returns each element of the initial set to itself.



Fig(i) Inverse function

Fractions:

A fraction is a number that can represent part of a whole. (source : Wikipedia)

In this article we are going to see about how to find the inverse functions with fractions and some solved problems on inverse functions with fractions.Please express your views of this topic how to find the range of a set of numbers by commenting on blog.

Problems on Inverse Functions with Fractions :
Problem 1:

Find the inverse of the following function with fraction f(x) = 6x /11– 25/ 22

Solution:

Given, f(x) = 6x /11– 25/ 22

Let us substitute f(x) = y

That is y = (6/11) x – 25/ 22

Let us make the common denominator,

Y = (6 * 2) x / (11*2) - 25 / 22

Y = 12x / 22 – 25 / 22

Y = (12x - 25) / 22

For finding the inverse function we have to solve for x,

Y = (12x - 25) / 22

Multiply by 22 on both sides,

22y = (12x - 25)

Add 25 on both sides,

22y + 25 = 12 x

Divided by 12 on both sides,

x = (22y + 25) / 12

Now replace y = x and x = f--1 (x)

f-1(x) = (22x + 25) / 12

Answer: Inverse function of a given function is f-1(x) = (22x + 25) / 12

Problem 2:

Find the inverse of the following function with fraction y = (4x-8)^2 / 3

Solution:

Given, y =  (4x-8)^2 / 3

For finding the inverse function we have to solve for x,

y =  (4x-8)^2 / 3

Multiply by 3 on both sides,

3y = (4x-8)^2

Taking square root on both sides,

`sqrt(3y)` =`sqrt((4x-8)^2)`

`sqrt(3y)` = 4x-8

Add 8 on both sides of the above equation,

`sqrt(3y)` + 8 = 4x -8 + 8

`sqrt(3y)` + 8 = 4x

4x = `sqrt(3y)` + 8

Divided by 4 on both sides of the above equation, we get

x =( `sqrt(3y)` + 8)/4

Substitute x =f-1(x) and y = x

f-1(x) =( `sqrt(3x)` + 8)/4

Answer: The inverse of a given function is f-1(x) =( `sqrt(3x)` + 8)/4

Prcatice Problems on Inverse Functions with Fractions :

Problems :

1. Find the inverse of a function with fraction f(x) = (x/2) + 5

2. Find the inverse of a function with fraction f(x) = ( x - 2)/5

Answer key:

1. f-1(x) = 2x - 10

2. f-1(x) = 2 + 5x