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determine whether each of these functions is a bijection from r to r. (16 points) a) f (x) = −3x 4 b) f (x) = −3x2 7

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Final answer:

To determine whether a function is a bijection from R to R, we need to check if it is both injective (one-to-one) and surjective (onto). For f(x) = -3x^4, the function is not injective. For f(x) = -3x^2/7, the function is not surjective.

Step-by-step explanation:

To determine whether a function is a bijection from R to R, we need to check if it is both injective (one-to-one) and surjective (onto).

a) For f(x) = -3x^4, we can see that this function is not injective because different values of x can map to the same output (-3x^4 = -3(-x)^4).

b) For f(x) = -3x^2/7, this function is also not a bijection as it is not surjective. The range of this function is (0, infinity), which means there are values in the codomain that are not covered by the function.

User Dan Baruch
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