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QUESTION: Hi! I have a question regarding functions:
How do you determine if this function is even, odd, or neither? Also, how do you determine if it is one to one?
f(x)= ln(2x-1)-3
Thanks!
Jenny
ANSWER: Hello Jenny
In order to check whether it is odd or even
First insert x and then –x in the function and analyze the results.
If f(-x) = -f(x) then this is an odd function
If f(-x) = f(x) then this is an even function
Now let’s check;
f(x)= ln(2x-1)-3
f(-x) = ln(-2X -1) -3
I don’t see any relation between them so I can say that it is neither.
Also if X and –X result in the same answer, then the function is not one to one.
Thankz
Michael
---------- FOLLOW-UP ----------
QUESTION: How can you determine if a piecewise function is even, odd, or neither? For example,
f(x)= x-1, x>1
0, -1 is less than or equal to x greater than or equal to 1
-x-1, x<-1
Hello again Jenny
To check if f(x)= x-1 is even or odd,
First substitute X in the function
f(X)= X-1
Now substitute -X in the function
f(-X)= -X-1
Now try to form a relation between the above two functions
f(X)= X-1 and f(-X)= -X-1
f(-X)= -f(X)-2
which is not the relation we want
As I told you before, if f(X) = f(-X), then the function is even
If f(-X) = -f(X), then the functions is odd.
Do you get my idea?
If you are still confused, I will try my best to give it my best shot again.
Thankz
Michael
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Answers by Expert:
Michael Tadesse
Expertise
I can answer questions regarding Relations, linear functions and equations, Squares and square roots, Translation and Similarity, Special Properties of Right Angled Triangles, Measurement of Area and Volume, algebra. I can also answer questions related to Pre calculus, Limits and Continuity, Derivatives Applications of Derivatives, High school math in general. I can’t answer questions of the following type. Power Series, Multiple Integrals, Fourier series, Vector valued Functions.
Experience
I love mathematics as it is the mother of all sciences. I had an outstanding math results while I was in school. The tradition continues while I am in university. I have been helping elementary school Students for the past five years with mathematics problems. In fact, I have a brother who is four years younger than me I usually help him to understand what the crux of the question is before trying to solve it. He loves math very much, he is indeed one of the top scorers form his class in Mathematics. I didn’t stop helping my younger relatives after I joined the Engineering campus and I am more than ready to help anyone with my skill.
Education/Credentials
have a high school diploma with a 3.97 GPA; I also have many merit certificates granted for my outstanding results in high school math. I won a merit certificate for my participation in the Black Month Essay Contest. I took two different National Examinations in 2006 and 2007. In the former Exam I got 9As which includes Mathematics. I also have a score of 90 out of hundred in the later Examination which is the toughest known in Ethiopia. So you don’t have to worry about my ability to help my clients.
Past/Present Clients
I have never had an online client but I was helping students coming to me for assistance in Mathematics.
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