If f(x)= x2+4x+4, then the domain of y= 1/f(x) is?
4 years ago
The domain is the set of all possible values of the independent variables. The independent variable is x. X can be anything => all real numbers.
f(x)=x2+4x+4=(x+2)2 >0 when x is a real number, so the domain of y=1/f(x) is all real numbers.
The only trick part to this question is the possibility of dividing by zero which causes the function to be undefined. To determine when the denominater is zero factor the function so it becomes f(x) = (x+2)(x+2) the only instance where you divide by zero is when x+2=0 or x=-2. This could be considered a restriction on the domain but it is just a singularity in the range where the function approached infinity.
so the corret answer shall be: the domain of y =1/f(x) is all real numbers except -2.
In general, for any function f(x) which is defined over the entire domain of real numbers, then 1/f(x) is also defined for all real numbers x EXCEPT those x for which f(x) = 0. If f(x) = 0 has no solution, then the domain of 1/f(x) is all real numbers.