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Stonybrook University Define Functions F and G from R to R Questions

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Stonybrook University Define Functions F and G from R to R Questions – Question Description

I’m working on a computer science practice test / quiz and need the explanation and answer to help me learn.

Define f: R -> R and g: R -> R by the following formulas: f(x) = |x| for all x ? R, g(x) = (x2)1/2 for all x ? R

Does f == g?

How many functions are there from a set with three elements to a set with four elements?

Define functions f and g from R to R by the formulas:

for all x ? R,

f(x) = 2x

g(x) = (2×3 + 2x)/(x2 + 1)

Show that f == g.

For f(x) = (x+1)/x for all real numbers where x != 0

a) Is this function onto?
b) Is this function one-to-one?

For f(x) = x/(x2 + 1) for all real numbers x

a) Is this function onto?
b) Is this function one-to-one?

How many one-to-one functions are there from a set with three elements to a set with four elements?

How many onto functions are there from a set with three elements tro a set with two elements?.

In a group of 30 people, at least how many must have been born in the same month?

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