What is the domain of f/g, given f(x)= x+2 and g(x)= x-7?
all real numbers EXCEPT 7
... division by zero is a NO-NO
How did you get that, @scott
My choices are this,
(-infinity,7) U (7,infinity)
(-infinity,-7) U (-7,infinity)
(-infinity,-2) U (-2,7)U (7,infinity)
((-infinity,infinity)
the domain of all polynomials is all real numbers.
But, division by zero is undefined, so any values of x that make the denominator zero must be excluded from the domain.
g(x) = x - 7
... when x = 7 , g(x) = 0
f/g is undefined
the 1st choice is correct
... there should be notation that 7 is NOT included
there is, but it's not interval notation. I'd say it's
{x|x∊R & x≠7}
To find the domain of f/g, we need to consider the values of x for which the division f(x)/g(x) is defined.
First, let's write the expression for f/g using the given functions:
f/g = (x+2)/(x-7)
Now, we need to determine the values of x that would make the denominator (x-7) equal to zero. This is because division by zero is undefined.
Setting the denominator equal to zero, we have:
x - 7 = 0
Solving for x, we find:
x = 7
Therefore, the value x = 7 should be excluded from the domain of f/g since it would result in division by zero.
In conclusion, the domain of f/g is all real numbers except for x = 7.