Find a bijection from (0,1] to (0,1) Math: Analysis and proof

Mathematics

1 answer:

gregori [183]3 years ago

8 0

Answer with explanation:

The meaning of bijection for two sets X and Y is each and every element of X is uniquely related with element of set Y and when you take the inverse mapping every element of set Y is uniquely related with each and every element of Set X.

The two sets given are

X=(0,1]---------Semi open or Semi closed Set

Y=(0,1)---------Closed set

Between any two real numbers there are infinite number of real numbers.So cardinal number of both the sets is infinite.

There can be infinite bijection between these two sets as both sets have infinite number of elements.

X Y

0.1 ------------- 0.01

0.2 ------- 0.02

0.3 -------- 0.03

0.4 --------- 0.04

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Use the parabola tool to graph the quadratic function f(x)=−5x2−2.

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$\text{Consider the quadratic function}\\
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f(x)=-5x^2-2\\
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h=\frac{-b}{2a}\\
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\text{on comparing the given equation with standard equation, we have}$

$a=-5, b=0, c=-2\\
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\text{so the x-coordinate of the vertex is }\\
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h=-\frac{b}{2a}=-\frac{0}{2(-5)}=0\\
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\text{so plug this vlaue of the h in the given function to get the y-coordinate}\\
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f(x)=-5(0)^2-2=0-2=-2\\
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