a Assume f A B is a function State the definition of onto b

(a) Assume f : A B is a function. State the definition of onto.

(b) Is the function f : R R; f(x) = 2x + 5 onto? Prove your

answers.

Each element in b has a corresponding element in a such that f(a)=b

Then f is called an onto function.

Let, y be a real number

Let, y=2x+5

Hence, x=(y-5)/2

So, f(x)=2(y-5)/2+5=y

Hence f is onto

c) No it is not onto.

2x+5 is always an odd integer for any integer x hence f is not onto.