How to determine the domain and range of the functions?

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autarhie6i · Accepted Answer

Definition of the Domain of a FunctionFor a function f defined by an expression with variable x, the implieddomain of f is the set of all real numbers variable x can take suchthat the expression defining the function is real. The domain can also be given explicitly.Example: Find the domain of function f definedbyf (x) = 1 / ( x - 5)x can take any real number except 5 since x = 5 would make the denominator equal to zero and the division by zero is not allowed in mathematics. Hence the domain in interval notation is given by   −  ∞  &amp;lt;  x  &amp;lt;  +  ∞ but, x 5Definition of the Range of a FunctionThe range of f is the set of all values that the function takes when x takes values in the domain.Example: Find the range of function f defined by:  f  (  x  )  =      x          2        −  2The domain of this function is the set of all real numbers. The range is the set ofvalues that f(x) takes as x varies. If x is a real number,      x          2       is either positive or zero. Hence we can write the following:      x          2        &amp;gt;=  0Subtract -2 to both sides to obtain      x          2        −  2  &amp;gt;=  −  2The last inequality indicates that       x          2        −  2 takes all values greater that or equal to -2. The range of f is given by[ -2 ,+infinity)

How to determine the domain and range of the functions?

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