Integration Area problem

Q4. find the region bounded by the two curves.

On QUORA

Mapping domain of composite functions question

f:R+ maps to R, f(x) = x to the power of -0.5, and g: R maps to R. g(x)=3-x.
a Show f(g(x)) is not defined
b restrict the domain to make a well defined function.

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Variance Question, year 12 Specialist in Victoria

Notes

The Question

Specifically

Specifically, the student has been given E(x) and tasked to find Var(5–3x). Their notes don’t actually cover it, neither does the textbook address it well.

A biased die with six sides is rolled. The discrete random variable X represents the score on the uppermost face. The probability distribution is shown in the table
c) Given E(x) = 4.2 find a and b
d) Show E(x squared) = 20.4
e) find Var(5–3x)
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From notes, Var (x) = E(x squared) - E((x) squared)
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Solution via Jan van Delden, MSc Math and still interested

Yes I can, now that I tried to read this elaborate link.

The point is that once you know var(𝑥)$\mathrm{var}(x)$ you should be able to apply a few basic rules of the variance operator in order to compute var(5–3𝑥)$\mathrm{var}(5–3x)$.

We have, with 𝑎$a$ a constant:

• var(𝑥+𝑎)=var(𝑥)$\mathrm{var}(x+a)=\mathrm{var}(x)$
• var(𝑎𝑥)=𝑎2var(𝑥)$\mathrm{var}(ax)=a^2\mathrm{var}(x)$

But first you should compute var(𝑥)$\mathrm{var}(x)$ using the equation, which is actually given to you in the link.