Range of a Function Calculator

The range of a real function of a real variable is the set of all real values taken by funtion f(x) at the points in its domain. In order to find the range of a real function f(x) using calculator we will use the following algorithm.

Put y=f(x)
Solve the equation y =f(x) for x in terms of y. Let x =phi(y)
Find the values of y for such that the values of x, obtained from x= phi(y) , are real and are in the domain of function f
The set of all such values of y obtained in the above step  is the range of function.


We use the above steps to find the range of a function using calculator.


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Examples on Range of Function Calculator:

Ex -1 Find the range of the function f(x) given by 1/(sqrt(x-5))

Solution We have f(x) = 1/(sqrt(x-5))

Let y = f(x)

y=1/(sqrt(x-5))

rArr y^2=1/(x-5)

rArr x-5 = 1/y^2

rArr x = 1/y^2 +5

It is clear that x assumes all real values except y=0

The range of the function is (0,oo )

Ex -2 Find the range of the function f(x) = 3/(2-x^2)

Solution: Given f(x) = 3/(2-x^2)

Let y = f(x) = 3/(2-x^2)

rArr y = 3/(2-x^2)

rArr 2-x^2 = 3/y

rArr 2-3/y = x^2

rArr (2y-3)/y = x^2

Taking square root on both sides

rArr x = sqrt((2y-3)/y)

x will take all values except -sqrt(2) and sqrt(2) , if (2y-3)/y>=0

rArr y in (-oo,0)U[3/2,oo)

This is the range of the function.


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Practice Problems on Range of Function Calculator:

Pro 1 Find the range of the function f(x) = (x^2-9)/(x-3)

Pro 2 Find the range of the function f(x) = (4-x)/(x-4)

Ans

1) Range of the function is R-{6}

2) Range of the function is {-1}