61). Domain for 8x+3/11-x. The book says it's -3/8 but I think it should be 11, so the denominator is zero. Why is this?
I think maybe you're getting two concepts mixed up, but I'm not quite sure.
The _domain_ is the set of values x can take. That is every real number_except_11, since it's undefined at x=11.
The _solution_ to
(8x+3)/(11-x) = 0
(aka the y-intercept of the graph)
is x = -3/8, because when x is -3/8, we have 8x+3 = 0, so the whole thing equals zero.
Thanks that really cleared it up! :)
To determine the domain of a rational function like 8x+3/(11-x), we need to consider the values of x for which the denominator is not equal to zero. The reason we exclude these values is because division by zero is undefined in mathematics.
In the given equation, the denominator is 11-x. To find the values of x that would make the denominator zero, we set 11-x equal to zero and solve for x.
11 - x = 0
By subtracting 11 from both sides, we get:
-x = -11
Dividing both sides by -1, we find:
x = 11
Therefore, x = 11 is the value that makes the denominator zero. Consequently, x = 11 should be excluded from the domain because it would result in division by zero.
The correct domain for the given rational function is all real numbers except x = 11. So, your book is correct, and the domain is NOT -3/8; it is all real numbers except x = 11.