d) neither one-to-one nor onto. 15. Determine whether each of these functions is a bijection from R to R. a) f (x) = 2x+1 b) f (x) = x2+1 c) f (x) r3 d) f (x) (x2 + 1) / (r2 + 2) a function f (x) - ex from the set of real

The only bijection is f (x) = 2x+1.

I took r to be a constant.

Step-by-step explanation:

Bijections are both onto and one-to-one.

Onto means every element of the codomain gets hit. Here the codomain is the set of real numbers. So you want every y to get hit.

One-to-one means you don't want any y to get hit more than once.

f (x) = 2x+1 is a linear function. It is diagonal line so every element of the codomain will get hit and hit only once so this function is onto and one-to-one.

f (x) = x^2+1 is a quadratic function. It is parabola so not every element of our codomain will get not get hit and of those that do get hit they get hit more than once. So this is neither onto or one-to-one.

f (x) = r^3 is a constant function. It is a horizontal line so not every y will get hit so it isn't onto. The same y is being hit multiple times so it isn't one-to-one.

f (x) = (x^2+1) / (r^2+2) is a quadratic. It is a parabola. Quadratic functions are not onto or one-to-one.