Answer:
Domain [-5,∞)
Range [0,∞)
Step-by-step explanation:
Part 1) Find the domain
we have

we know that
The radicand must be greater than or equal to zero
so

solve for x
subtract 5 both sides

The solution for x is the interval [-5,∞)
All real numbers greater than or equal to -5
Remember that
The domain of a function is the set of all possible values of x
therefore
The domain of the function f(x) is the interval [-5,∞)
Part 2) Find the range
we have

Find the value of f(x) for the minimum value of x
For x=-5


The minimum value of f(x) is equal to zero
so
The solution for f(x) is the interval [0,∞)
All real numbers greater than or equal to 0
Remember that
The range of a function is the complete set of all possible resulting values of y, after we have substituted the domain.
therefore
The range of the function is the interval [0,∞)
Answer:
They made 4 forks and 6 spoons last April.
Step-by-step explanation:
Let forks they made in april be x and spoons be y.
To make 1 fork we need $2
To make 1 spoon we need $1
They sell 1 fork for $6 and 1 spoon for the same amount So,
now,
Turning it into two equations :-
(x = number of forks and y = number of spoons)
2x + 1y = 14
6x + 6y = 60
Now,
2x + y = 14
y = 14 - 2x
Now,
6x + 6y = 60
or, 6x + 6(14-2x) = 60
or, 6x + 84 - 12x = 60
or, -6x = -24
so, x = 4
Now,
y = 14 - 2x
or, y = 14 - 2×4
or, y = 14-8
so, y = 6