Answer:
a =1 and a=4.
Step-by-step explanation:
The function is
![f(x)=\frac{(x-1)(x^2-4)}{x^2-a}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B%28x-1%29%28x%5E2-4%29%7D%7Bx%5E2-a%7D)
If we want f(x) to be continuous the denominator needs to be different to 0, otherwise f(x) will be indeterminate.
Now, for a a positive real we have that
will annulate the denominator, i.e
. But, if a = 1 we have:
![f(x)=\frac{(x-1)(x^2-4)}{x^2-1} = \frac{(x-1)(x^2-4)}{(x-1)(x+1)}=\frac{(x^2-4)}{x+1}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B%28x-1%29%28x%5E2-4%29%7D%7Bx%5E2-1%7D%20%3D%20%5Cfrac%7B%28x-1%29%28x%5E2-4%29%7D%7B%28x-1%29%28x%2B1%29%7D%3D%5Cfrac%7B%28x%5E2-4%29%7D%7Bx%2B1%7D)
so, the value
won't annulate the denominator.
Now, for a = 4 we have:
![f(x)=\frac{(x-1)(x^2-4)}{x^2-4} = x-1](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B%28x-1%29%28x%5E2-4%29%7D%7Bx%5E2-4%7D%20%3D%20x-1)
so, the value
won't annulate the denominator.
In conclusion, for a=1 or a=1, the function will be continuos for all real numbers, since the denominator will never be 0.
Answer:
C
Step-by-step explanation:
6x^2 + 2x - 8
Multiply the (6) to the -(8) to get x^2 by itself.
x^2 + 2x - 48
Solve -
(x-6)(x+8) = x^2 + 2x - 48
However, you must divide out the (6) you multiplied.
(x-6/6) =
(x-1)
(x+8/6) =
(3x + 4)
Therefore, 2(3x + 4)(x-1) is your answer.
EDIT - At the beginning of the equation it is possible to divide (2) out of the equation, this is where the (2) at the end comes from.
Answer:
???????
Step-by-step explanation:
It’s the second option counting from top to bottom
Answer:
1: 250 000
( There are 1000 metres in a km and 100 cm in a m, thus you multiply 5 km by 100 000 to convert it to cm, then you divide by 2 in order to get the simplist form of the ratio )