Question

Construct examples
a. show that if f and g are one to one, then f+g might not be one-to-one.
b. show that if f and g are onto, then f+g need not be onto.
c. give an example of functions f and g that are one to one and onto, but f times g is not one to one and not onto.

Answer 1

how many times are you going to ask this question?

Answer 2

part a) hint: pick a one to one function for f, it can be any. then for g pick its negative.
if you add them what do you get?

Answer 3

For example
f(x) = e^x + 1
g(x) = -e^x

both functions are one to one. What happens when you add the functions

Answer 4

Actually a simpler function is
f(x) = x
g(x) = -x

f and g are both one to one and onto. However f(x) + g(x) = 0 which is a constant function. The constant function is neither one to one nor onto.

Answer 5

f times g is neither one to one nor onto as well

Answer 6

@perl the user keeps posting the question under many different names, and refuses to take part