1. ## proof question

I'm assuming that the second sentence in each of these paragraphs is a proof, but I have no idea how to comprehend them. Help please.

2. Hello khor
Originally Posted by khor

I'm assuming that the second sentence in each of these paragraphs is a proof, but I have no idea how to comprehend them. Help please.
I'm not quite sure what you mean by "... is a proof." The second sentence in the first paragraph (and the third sentence in the second paragraph) is a statement, followed by an explanation of why that statement is true.

The first one is:
Statement

• The range of $\displaystyle y = x^2$ is $\displaystyle [0,\infty)$

Explanation

• The square of any real number is non-negative (in other words the range can't contain any negative numbers)

• Every non-negative number is the square of its own square root (in other words, every non-negative number is included in the range because there will always exist a corresponding element in the domain, namely, its square root)
The second one is:
Statement

• The range of $\displaystyle y = 1/x$ ... is the set of all non-zero real numbers.

Explanation

• $\displaystyle y = 1/(1/y)$ (in other words, the reciprocal function is its own inverse. So, since the domain of $\displaystyle y = 1/x$ is all non-zero real numbers the range will also be all non-zero real numbers)
I hope that is what you wanted.

(and the third sentence in the second paragraph)

Ooops, I mean third sentence there yeah.

(in other words, the reciprocal function is its own inverse. So, since the domain of $\displaystyle y = 1/x$ is all non-zero real numbers the range will also be all non-zero real numbers)