Question 2:

given the following functions:

f(x) = x^2

g(x) = x - 3

find the composition of the two functions and show your process:

g(f(x))

question 3:

if the composition of two functions is:

1
x - 3

what would be the domain restriction? describe how you found that answer.

2:

3: x ≠ 3

Step-by-step explanation:

2 : Here the given functions,

( From equation (1) ),

    ( From equation (2) )

3 :

Since, it is a rational function,

A rational function is defined for all real numbers except those for which,

Denominator = 0,

If x - 3 = 0

⇒ x = 3

So, Domain of h(x) = R - {3}

i.e., the domain restriction for h(x) is x ≠ 3

constant of proportionality = 3 and the equation is c = 3p.

step-by-step explanation:

c = kp   where c = amount of caffeine in mg., p = oz of pepsi and k is the constant of proportionality.

substituting the values given:

24 = 8k

k = 3.

the same value of k will be obtained if we substitute the other given values.

answer: the sun

explanation:

water cycle describes the evaporation of water from earth's surface, formation of clouds and precipitation water back onto the surface of earth. seventy percent of the earth is covered with water in the form of seas and oceans. the heat of the sun causes the evaporation of water from the surface of the ocean. the water vapors rise and condense to form water droplets. the collection of these water droplets form clouds which rain down again.

the evaporation of the oceans surface water as part of the water cycle is caused by the sun