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Differential Calculus
31 May 2007 17:26:21 IST
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T RAHUL N THIRUGNANAM
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Joined: 23 Mar 2007
Posts: 85
31 May 2007 17:28:42 IST
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u hav to use f(x)=y.Find x in terms of y.Now put various values of y such tha t the func satisfies.U will get the range
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31 May 2007 18:10:41 IST
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range of a function f(x) is defined as the set of all possible values that f(x) can take for values of x belonging to domain!!!!
example
Find the range of function f defined by: f (x) = x 2 - 2
The domain of this function is the set of all real numbers. The range is the set of values that f(x) takes as x varies. If x is a real number, x2 is either positive or zero. Hence we can write the following:
x 2 >= 0
x 2 >= 0
Subtract -2 to both sides to obtain
x 2 - 2>= -2
The last inequality indicates that x2- 2 takes all values greater that or equal to -2. The range of f is given by
[ -2 , +infinity)
x 2 - 2>= -2
The last inequality indicates that x2- 2 takes all values greater that or equal to -2. The range of f is given by
[ -2 , +infinity)
A graph of f also helps in interpreting the range of a function. Below is shown the graph of function f given above. Note the lowest point in the graph has a y (= f (x) ) value of -2.
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