The quadratic function y = –2(x + 4)2 – 3 with no real zeros is graphed.
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Answer:
- When we are having a rational expression i.e. a expression of the type:
Where f(x) and g(x) are polynomial functions.
Now the domain of this rational expression is whole of the real numbers except the points where the function g(x) will be zero.
Hence we have to exclude the points where the given denominator quantity is zero.
- Let us consider an example as:
Let R(x) denote the rational function as:
Now the domain of this rational function will be whole of the real line minus the points where the denominator is zero.
We know that (x-2)(x-3) is zero when x=2 or x=3.
Hence, the domain of R(x) is: R- {2,3}.
Example:
This suggests two solutions,
and 
.
However, upon plugging these solutions back into the equation, you get
which checks out, but
does not because
is defined only for 
(assuming you're looking for real solutions only). So, we call an extraneous solution, and the complete solution set (over the real numbers) is .
This suggests two solutions,
However, upon plugging these solutions back into the equation, you get
which checks out, but
does not because