What is the domain of f/g, given f(x)= x+2 and g(x)= x-7?
I was told this below,
all real numbers EXCEPT 7
But
My choices are this,
(-infinity,7) U (7,infinity)
(-infinity,-7) U (-7,infinity)
(-infinity,-2) U (-2,7)U (7,infinity)
(-infinity,infinity)
well, yeah.
(-∞,∞) is all real numbers.
So, how do you get x=7 out of there? You divide it up into two intervals, each excluding x=7
So, whaddaya think?
there is something about the shape of the parentheses/brackets that excludes one end of an interval
sorry...rusty on this part
Is it A then steve??
that is correct. The () interval notation indicates that the endpoints are not included.
To find the domain of the function f/g, you need to consider the restrictions that apply. In this case, the denominator of the function is g(x), which is x - 7.
To determine the domain, you need to exclude any values of x that would make the denominator equal to zero. This is because division by zero is undefined.
In the given scenario, the denominator would be zero when x = 7. Therefore, the domain of f/g is all real numbers except for x = 7.
Out of the choices you provided, the correct one is:
(-∞, 7) U (7, ∞)
This represents all real numbers from negative infinity to less than 7, excluding 7, and all real numbers greater than 7 to positive infinity.