Could you please check my answers and help me with one?
Find the domain of the function.
f(x)=-8x-2
-I got the domain being (negative infinity, postive infinity).
g(x)= 3x/x^2 -49 (This one I don't understand how to find the domain)
yes on domain
I assume the second is g(x)=3x/(x^2-49)
can x be +-7 ?
I try to figure out it, and since x^2-7 is a perfect square (x+7)(x-7), I thought x couldn't be +-7?
Sure, I'd be happy to help you with your question.
For the function f(x) = -8x - 2, you are correct in determining that the domain is (-∞, ∞), which means that there are no restrictions on the possible values of x.
Now let's look at the function g(x) = 3x/(x^2 - 49). To find the domain, we need to consider any restrictions on x that would cause the function to become undefined.
In this case, the function is not defined when the denominator (x^2 - 49) equals zero because division by zero is undefined. To find the values of x that make the denominator zero, we can set the denominator equal to zero and solve for x.
x^2 - 49 = 0
Now, let's factor the quadratic equation:
(x - 7)(x + 7) = 0
Setting each factor to zero:
x - 7 = 0 or x + 7 = 0
Solving for x:
x = 7 or x = -7
So, we have two values of x, x = 7 and x = -7, which make the denominator equal to zero. These are the values that we need to exclude from the domain since they would make the function undefined.
Therefore, the domain of g(x) is all real numbers except x = 7 and x = -7. In interval notation, we can represent the domain as (-∞, -7) U (-7, 7) U (7, ∞).