Show that the Signum Function f: R → R, given by
answer it correctly
Answers
Answer:
f(x)=⎧⎩⎨⎪⎪10−1for x>0for x=0 is neither one−one nor ontofor x<0
Solution:
Check for one to one function:
For example:
f(0) = 0
f(-1) = -1
f(1) = 1
f(2) = 1
f(3) = 1
Since, for the different elements say f(1), f(2) and f(3), it shows the same image, then the function is not one to one function.
Check for Onto Function:
For the function,f: R →R
f(x)=⎧⎩⎨⎪⎪10−1for x>0for x=0for x<0
In this case, the value of f(x) is defined only if x is 1, 0, -1
For any other real numbers(for example y = 2, y = 100) there is no corresponding element x.
Thus, the function “f” is not onto function.
Hence, the given function “f” is neither one-one nor onto.
Answer:
f(x)=⎧⎩⎨⎪⎪10−1for x>0for x=0 is neither one−one nor ontofor x<0
Solution:
Check for one to one function:
For example:
f(0) = 0
f(-1) = -1
f(1) = 1
f(2) = 1
f(3) = 1
Since, for the different elements say f(1), f(2) and f(3), it shows the same image, then the function is not one to one function.
Check for Onto Function:
For the function,f: R →R
f(x)=⎧⎩⎨⎪⎪10−1for x>0for x=0for x<0
In this case, the value of f(x) is defined only if x is 1, 0, -1
For any other real numbers(for example y = 2, y = 100) there is no corresponding element x.
Thus, the function “f” is not onto function
Hence, the given function “f” is neither one-one nor onto.