What are the domain and range of f (x) = (one-fifth) Superscript x?
2 answers:
Answer:
The domain of the function is all real numbers and the range is all positive real numbers
Step-by-step explanation:
We have the following function and we want to find the domain and the range.
The function we have is an example of an exponential function with b > 0 and b ≠ 1. This types of functions in general have the following properties:
- It is always greater than 0, and never crosses the x-axis
- Its domain is the set of real numbers
- Its Range is the Positive Real Numbers
The domain of a function is the specific set of values that the independent variable in a function can take on.
When determining domain it is more convenient to determine where the function would not exist.
This function has no undefined points nor domain constraints. Therefore the domain is .
The range is the resulting values that the dependent variable can have as x varies throughout the domain. Therefore the range is .
We can check our results with the graph of the function.
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Answer:
minimum cost of construction box are x = x = 3.4199 in and y = 10.2598 in and z = 4.2750 in
Step-by-step explanation:
given data
volume = 150 in³
base material costing = 5 cents/in²
front cost = 10 cents/in²
remainder sides cost = 2 cents/in²
to find out
the dimensions that will minimize the cost
solution
we consider here length = x and breadth = y and height = z
and
area of base = xy
area of front = xz
and area of remaining side = xz + 2yz .....................1
so
cost of base will be = 5xy
cost of front = 10xz
cost of remaining side = 2 ( xz+ 2yz)
and
total cost will be
total cost TC = 5xy + 10xz + 2 ( xz+ 2yz)
total cost TC = 5xy + 10xz + 2xz+ 4yz
total cost TC = 5xy + 12xz + 4yz ....................2
and total volume will be = xyz
150 = xyz
z = .......................3
now put z value in equation 2
total cost TC = 5xy + 12xz + 4yz
total cost TC = 5xy + 12x + 4y
total cost TC = 5xy + +
...........4
now differentiate TC w.r.t x and y
TC (x) = 5y -
TC (x) = 5x -
now equating with 0 these
5y - = 0
x² =
and
5x - = 0
x =
solve we get
y = 10.2598
x = 3.4199
now put x and y value in equation 3
z =
z =
z = 4.2750
so minimum cost of construction box are x = x = 3.4199 in and y = 10.2598 in and z = 4.2750 in