## INVERSE FUNCTIONS USING TABLES

Inverse Functions Using Tables :

Here we are going to see, how we find inverse functions using tables.

For functions whose domain consists of only finitely many numbers, tables provide good insight into the notion of an inverse function.

Suppose f is a function defined by a table. Then:

• f is one-to-one if and only if the table defining f has no repetitions in the second column.
• If f is one-to-one, then the table for f −1 is obtained by interchanging the columns of the table defining f.

Let us look into some example problems to understand the concept.

## Inverse Functions Using Tables - Examples

Question 1 :

Suppose f is the function whose domain is the four numbers {√2, 8, 17, 18}, with the values of f given in the table shown here in the margin.

(a) What is the range of f ?

(b) Explain why f is a one-to-one function.

(c) What is the table for the function f −1?

Solution :

(a) From the table x represents domain and f(x) represents range. Hence the range of the function is {3, -5, 6, 1}.

(b)  From the table, we know that every element of x is associated with unique elements of f(x). Hence it is one to one function.

(c)  From the table, we understood that

f(√2)  =  3, f(8)  =  -5, f(17)  =  6, f(18)  =  1

f-1(3)  =  √2, f-1(-5)  =  8, f-1(6)  =  17, f-1(1)  =  18

Question 2 :

For f and g are functions, each of whose domain consists of four numbers, with f and g defined by the tables below:

(a)  What is the domain of f ?

(b)  What is the range of f ?

(c)  Give the table of values for f−1.

(d)  What is the domain of f−1?

(e)  What is the range of f−1?

(f)  Sketch the graph of f and f-1

(g)  Give the table of values for f−1 ◦ f

Solution :

(a)  Domain of f  =  {1, 2, 3, 4}

(b)  Range of f  =  {2, 3, 4, 5}

(c)  Give the table of values for f−1.

(d)  domain of f-1 =  {2, 3, 4, 5}

(e)  Range of f-1  =  {1, 2, 3, 4}

(f)  From the graph, we know that the inverse function is reflection of the function.

(g)  Give the table of values for f◦f−1

(f◦f −1)(2) = f (f−1(2)) = f(3) = 2

(f◦f −1)(3) = f(f−1(3)) = f(4) = 3

(f◦f−1)(4) = f(f −1(4)) = f(1) = 4

(f◦f −1)(5) = f(f−1(5)) = f(2) = 5

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

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

You can also visit our following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Word problems on quadratic 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