Find the domain for the rational function f(x)=x-1/x+3
1 answer:
Answer:
x≠-3 or x<-3 and -3<x or (∞,-3) and (-3,∞)
Step-by-step explanation:
If the expression you have given is then the domain is x≠-3
This is because in a function that is a fraction the denominator can never equal 0, otherwise you are dividing by 0 which is undefined.
Here the denominator is x+3 and so to find the undefined value of x:
Set x+3 equal to 0:
x+3=0
Subtract 3:
⇒ x=-3
That value is undefined since it results in the division of 0 which also means that it is not in the domain.
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We have two points:
The point slope form of the line:
Substitute
Answer:
Step-by-step explanation:
Take the first derivative
Set the derivative equal to 0.
or
For any number less than -1, the derivative function will have a Positve number thus a Positve slope for f(x).
For any number, between -1 and 1, the derivative slope will have a negative , thus a negative slope.
Since we are going to Positve to negative slope, we have a local max at x=-1
Plug in -1 for x into the original function
So the local max is 2 and occurs at x=-1,
For any number greater than 1, we have a Positve number for the derivative function we have a Positve slope.
Since we are going to decreasing to increasing, we have minimum at x=1,
Plug in 1 for x into original function
So the local min occurs at -2, at x=1