Suppose A is an uncountable set and B is a denumerable set. Suppose f:A→B is a function. Prove that for at least one bEB, f-1(b) = {xEA | f(x)=b} is uncountable.

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A: Questions from real analysis.

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A: Hi, you can find the answer in the handwritten form.  Given f(a)=-2  f(b)= 2

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: