given: f(x) = (x + 2)/x and g(x) = (x + 1)/(x + 2)
what is the domain of f(x) times g(x)?
X is all except 0(because of f(x)) and -2 (because of g(x))
g=6 and x=2
would the domain for f(x) over g(x) be the same??
f(x)*g(x) = (x+1)/(x)
only explodes when x = 0
f(x) / g(x) = [(x+2)(x+2)] / [x (x+1) ]
this one blows up at x = 0 and x = -1
To find the domain of f(x) times g(x), we need to find the values of x for which both functions are defined.
Let's start by finding the domain of f(x). The only restriction for f(x) is that the denominator (x) cannot be zero since division by zero is undefined. So, we can say that the domain of f(x) is all real numbers except x = 0.
Next, let's find the domain of g(x). Similar to f(x), the denominator (x + 2) cannot be zero. Therefore, we can say that the domain of g(x) is all real numbers except x = -2.
To determine the domain of f(x) times g(x), we need to find the values of x that satisfy the restrictions of both f(x) and g(x). In other words, we need to find the values of x that are not equal to 0 or -2.
Since there are no other restrictions on the functions, we can conclude that the domain of f(x) times g(x) is all real numbers except x = 0 and x = -2.