Consider the following functions. f(x) = x − 3, g(x) = x2 Find (f + g)(x). Find the domain of (f + g)(x). (Enter your answer using interval notation.) Find (f − g)(x). Find the domain of (f − g)(x). (Enter your answer using interval notation.) Find (fg)(x). Find the domain of (fg)(x). (Enter your answer using interval notation.) Find f g (x). Find the domain of f g (x). (Enter your answer using interval notation.)
Answers
Answer:
; Domain = (-∞, ∞)
; Domain = (-∞, ∞)
; Domain = (-∞, ∞)
; Domain = (-∞,0)∪(0, ∞)
Step-by-step explanation:
The given functions are
1.
Substitute the values of the given functions.
The function is a polynomial which is defined for all real values x.
Domain of (f+g)(x) = (-∞, ∞)
2.
Substitute the values of the given functions.
The function is a polynomial which is defined for all real values x.
Domain of (f-g)(x) = (-∞, ∞)
3.
Substitute the values of the given functions.
The function is a polynomial which is defined for all real values x.
Domain of (fg)(x) = (-∞, ∞)
4.
Substitute the values of the given functions.
The function is a rational function which is defined for all real values x except 0.
Domain of (f/g)(x) = (-∞,0)∪(0, ∞)
, domain: all real numbers.
, domain: all real numbers.
, domain: all real numbers.
, domain: all real numbers.
To find (f + g)(x), we need to add the functions f(x) and g(x).
The function f(x) = x - 3 and the function
So,
Expanding this equation, we get
To find the domain of (f + g)(x), we need to consider the domain of the individual functions f(x) and g(x).
Since both f(x) = x - 3 and are defined for all real numbers, the domain of (f + g)(x) is also all real numbers.
To find (f - g)(x), we need to subtract the function g(x) from f(x).
So,
Expanding this equation, we get
The domain of (f - g)(x) is also all real numbers, since both f(x) and g(x) are defined for all real numbers.
To find (fg)(x), we need to multiply the functions f(x) and g(x).
So,
Expanding this equation, we get
The domain of (fg)(x) is all real numbers, since both f(x) and g(x) are defined for all real numbers.
To find f(g(x)), we need to substitute g(x) into the function f(x).
So,
The domain of f(g(x)) is also all real numbers, as is defined for all real numbers, and f(x) = x - 3 is defined for all real numbers.
In summary:
- , domain: all real numbers.
- , domain: all real numbers.
- , domain: all real numbers.
- , domain: all real numbers.
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Related Questions
The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 261.5 and a standard deviation of 67.4 . (All units are 1000 cells/μL.) Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of women with platelet counts within 1 standard deviation of the mean, or between 194.1 and 328.9 ? b. What is the approximate percentage of women with platelet counts between 59.3 and 463.7 ?
Please helpdetermine all the unknown values of the figure below.
If you know if try to answer its fine if you cant
A fair coin is tossed 25 times. what is the probability that at most 24 heads occur?
1) (0,5) and (1,6)
2) (0,5) and (-1,0)
3) (2.9) and (-1,4)
4) (-2,9) and (-1.4)
Answers
Answers
Answer:
50%
Step-by-step explanation:
Let :
Winter = W
Summer = S
P(W) = 0.85
P(S) = 0.65
Recall:
P(W u S) = p(W) + p(S) - p(W n S)
Since, none of them did not like both seasons, P(W u S) = 1
Hence,
1 = 0.85 + 0.65 - p(both)
p(both) = 0.85 + 0.65 - 1
p(both) = 1.50 - 1
p(both) = 0.5
Hence percentage who like both = 0.5 * 100% = 50%
Answers
Answer:
31 ft
Step-by-step explanation:
The statue represents the side of a right triangle that is opposite the angle of elevation. The distance to the statue represents the side adjacent to the angle. Then ...
Tan = Opposite/Adjacent
tan(61°) = h/(17 ft)
Multiplying by 17 ft, we have ...
h = (17 ft)tan(61°) ≈ 30.67 ft
h ≈ 31 feet
Answers
Answer:
7.8 i
Step-by-step explanation:
Since -61 is negative, you simply do the square root of positive 61 and add an i (imaginary) so signify that it's negative.
Answers
There are 256 cubic inches of water in the vase.
How many cubic inches of water are in the vase?
We know that the volume of a cube with side length S is:
V = S^3
In this case, we know that S = 8in, then the volume is:
V = (8 in)^3 = 512 in^3
And we know that it is half full with water, so the volume of water in the vase is:
V' = (512 in^3)/2 = 256 in^3
If you want to learn more about volume, you can read:
Answer:
256
Step-by-step explanation:
First find the volume of the cube, which is 8^3, or 512. Half of that is how much water there is, which is 256 in^3.
Answers
Answer:
240 cartons
Step-by-step explanation:
If the bars will be packed in cartons which are 1 foot wide, 1 foot high, and 1 foot long, the volume of the carton will be expressed as shown;
Volume of carton = Length * Breadth * Height
Volume of carton = 1ft*1ft*1ft
= 1ft³
Given the dimension of shipping crate to be 5 ft long, 12 ft wide, and 4 ft high, the volume of the tank will be 5*12*4 = 240ft³
Number of cartons they pack into the shipping crate = Volume of the shipping crate/volume of one carton
Number of cartons they pack into the shipping crate = 240ft³/1ft³
= 240 cartons
Answer:
number of cartons that can be packed in the shipping crate = 240 cartons
Step-by-step explanation:
The cartons are cube since the face all have the same dimension . The length = 1 ft, width = 1 ft and height = 1 ft.
The shipping crate is a rectangular prism or cuboid . The dimension is given as follows.
length = 5 ft
width = 12 ft
height = 4 ft
The number of the cartons that can be packed in the shipping crate can be calculated as follows.
volume of the cubed carton = L³
where
L = length
volume of the cubed carton = 1³ = 1 ft³
Volume of the shipping crate = LWH
where
L = length
W = width
H = height
Volume of the shipping crate = 5 × 12 × 4
Volume of the shipping crate = 240 ft³
number of cartons that can be packed in the shipping crate = 240/1 = 240 cartons