Let f(x) = 4x and g(x) = x + 6. What's
the smallest number that is in the domain of
fºg?

For this case we have the following functions:

By definition of composition of functions we have to:

So:

By definition, the domain of a function is given by all the values for which the function is defined. The compound functionis defined for all real numbers.

The domain of is given by all real numbers.

Domain ∈ (-∞,∞)

the solution is 12x-6y

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.