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denpristay [2]
4 years ago
5

Supposef:ZZ is defined by f(x) = 2x^2 + 1. a. Explain using the definition of onto functions why the function f is or is not an

onto function b. Explain using the definition of one-to-one functions why the function f is or is not a 1-1 function
Mathematics
1 answer:
Black_prince [1.1K]4 years ago
6 0

a. Since f:\Bbb Z\to\Bbb z, the function f(x)=2x^2+1 is not onto because not every element in the codomain \Bbb Z is represented by f(x). For any x\in Z, we have x^2\ge0, so x^2+1\ge1, which means there is no choice of x such that f(x)\le0.

b. f is not one-to-one because there are infinitely many choices of x for which f(-x)=f(x). For example, f(1)=1^2+1=2 and f(-1)=(-1)^2+1=2.

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