For each of these functions is it onetoone Is it onto For ea

For each of these functions, is it one-to-one? Is it onto?

For each of these functions, is it one-to-one? Is it onto? For each of these functions, is it one-to-one? Is it onto? (recall that the range [0. infinite) is the non-negative real numbers) f1: [0, infinite) right arrow [0, infinite); f1(x) =x^2 f2: [0, infinite) right arrow [0, infinite); f2(x) = (x -1)^2 f3: [0, infinite) right arrow [0, infinite); f3(x) = x^2 + 1 f4: [0, infinite) right arrow [0, infinite); f4(x) = (x - 1)^2 + 1

Solution

f1 is not one to one as -x and x have the same image.

Not onto as range is not negative R

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f2 not one to one and not onto. as range is R+

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f3: Range is only R+ and x and -x have the same image. Hence not oneto one nor onto

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f4: Range is only R+ and x and -x have the same image. Hence not oneto one nor onto