3 questions
https://web2.0calc.com/questions/we-define-a-function-f-x-such-that-f-11-34-and-if
and
Find the domain of \(\frac{x^2 + 10x + 21}{x^2 + 4x - 21}\) (Express your answer using interval notation.)
and
Let \(f(x) = \left\lceil\dfrac{1}{x+2}\right\rceil\) for \(x > -2\), and \(f(x) = \left\lfloor\dfrac{1}{x+2}\right\rfloor\) for \(x < -2\). ( is not defined at \(x = -2\).) Which integer is not in the range of \(f(x)\)?
+128472 [ x^2 + 10x + 21]
______________
[ x^2 + 4x - 21 ]
The domain excludes any x values that makes the denominator = 0
So
x^2 + 4x - 21 = 0
(x + 7) ( x - 3) = 0
Setting each factor to 0 and solving for x produces the two x values not in the domain ⇒
x = - 7 and x = 3
So.....the domain is
(-inf, -7) U (-7, 3) U (3, inf)
