If function f is defined from set of real numbers R to R in the following way then classify them in the form of one-one, many-one, into or onto.

A function f from the set of natural numbers to integers is defined by n when n is odd f(n)3, when n is even Then f is (b) one-one but not onto a) neither one-one nor onto (c) onto but not one-one (d) one-one and onto both

A function f from the set of natural numbers to integers is defined by n when n is odd f(n) =3, when n is even Then f is (b) one-one but not onto a) neither one-one nor onto (c) onto but not one-one (d) one-one and onto both

If R is the set of real numbers and a function f: R to R is defined as f(x)=x^(2), x in R , then prove that f is many-one into function.

Classify the following functions in the form of one-one,many one,into and onto,also give reason to support your answer.

Let f:R to R .is a function which is defined by f(x)=x^2 a. one-one b. many-one c. onto d. into

If f:R to R be defined by f(x) =2x+sinx for x in R , then check the nature of the function. a. one-to-one and onto b. one-to-one but not onto c. onto but not one-to-one d. neither one-to-one nor onto

Let M be the set of all 2xx2 matrices with entries from the set R of real numbers. Then the function f: M->R defined by f(A)=|A| for every A in M , is (a) one-one and onto (b) neither one-one nor onto (c) one-one but not onto (d) onto but not one-one

Let M be the set of all 2xx2 matrices with entries from the set R of real numbers. Then the function f: M->R defined by f(A)=|A| for every A in M , is (a) one-one and onto (b) neither one-one nor onto (c) one-one but not onto (d) onto but not one-one

If R is the set of real numbers then prove that a function f: R to R defined as f(x)=(1)/(x), x ne 0, x in R, is one-one onto.

If R is the set of real numbers then prove that a function f: R to R defined as f(x)=(1)/(x), x ne 0, x in R, is one-one onto.