Even and odd functions:
If f: X→Y is a original valued function such that for all x∈D => - x ∈ D (where D = domain of f) and if f(- x) = f(x) for every x∈D then f is called an even function and if f(- x) = - f(x) then f is called be odd function.
MORE IMPORTANT POINTS:
- Even functions are symmetric with related to the y - axis (i.e. if (x, y) lies on the curve, then (- x, y) also lies on the curve).
- Odd functions are symmetric about the origin and it is located either in the first and third quadrant or in the second and fourth quadrant. (i.e. if (x, y) place in between on the graph, then (- x, - y) also lies on the curve).
- f(x) = 0 is the only function which is both odd and even.
- If f(x) is an odd function, then f(x) is an odd function shown f(x) is differentiable on R.
- To express a provided function f(x) as the summation of an odd and even function, we write
is an even function and 
is an odd function.
- If x = 0 ∈ domain of f, then for odd function f(x), f(0) = 0 i.e. but for a function, f(0) ≠ 0, then that function may not be odd.
Problem: Which of the subsequent functions is (are) odd, even or neither :
Solution:
Email based Even and odd functions Assignment Help -Even and odd functions Homework Help
We at www.expertsmind.com offer email based Even and odd functions assignment help - homework help and projects assistance from k-12 school level to university and college level and engineering and management studies. We provide finest service of Mathematics assignment help and Mathematic homework help. Our experts are helping students in their studies and they offer instantaneous tutoring assistance giving their best practiced knowledge and spreading their world class education services through e-Learning program.
Expertsmind's best education services
- Quality assignment-homework help assistance 24x7 hrs
- Best qualified tutor's network
- Time on delivery
- Quality assurance before delivery
- 100% originality and fresh work