Show that the statement, "if f and gof are one-to-one, then g is one-to-one", is not true.

Show that if f: A to B and g : B to C are one-one, then gof :A to C is also one-one.

Give an example, such that if f and: gcircf are one-one then g need not be one-one.

Let f: A to B and g: B to C be two functions. Then; if gof is onto then g is onto; if gof is one one then f is one-one and if gof is onto and g is one one then f is onto and if gof is one one and f is onto then g is one one.

Which of the following statements are incorrect? 1.If f(x) and g(x) are one-one then 2. f(x)+g(x) is also one-one If f(x) and g(x) are one-one then 3. f(x)dotg(x) is also one-one If f(x) is odd then it is necessarily one-one? Ia n dI Ion l y b. I Ia n dI I Ion l y c. I I Ia n dIon l y d. I ,I Ia n dI I I

Which one of the following is not true?

Which one of the following is not true?