FIND RANGE OF FUNCTION FOR GIVEN DOMAIN

Domain :

The domain of a function f(x) is the set of all values for which the function is defined

Range :

The range of the function is the set of all values that f takes.

They may also have been called the input and output of the function.) .

It is like evaluating functions for the given value of x.

Example 1 :

Consider f(x)  =  x² for the domain {-2, -1, 0, 1, 2}

Find the range.

Solution :

Given, f(x)  =  x²

Range  =  {4, 1, 0, 1, 4}

Example 2 :

For the following functions of

f : x -> f(x) on -2≤x≤2

where x ∈ z

(a)  List the elements of the domain of f(x) using set notation.

(b)  List the elements of the range of f(x) using set notation.

(1)  f(x)  =  1/(x+3)   

(2)  (x+3)/x  and x ≠ 0

 (3)  f(x)  =  3^x

(1)  Solution :

Given :

f(x)  =  1/(x+3)

Domain  =  {-2, -1, 0, 1, 2}

Range  =  {1, 1/2, 1/3, 1/4, 1/5}

(2)  Solution :

Given :

f(x)  =  (x+3)/x

Domain  =  {-2, -1, 0, 1, 2}

Range  =  {-1/2, -2, 5/2, 4}

(3)  Solution :

Given :

f(x)  =  3^x

Domain  =  {-2, -1, 0, 1, 2}

Range  =  {1/9, 1/3, 1, 3, 9}

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