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ratelena [41]
3 years ago
11

If f(x) = x + 4 and g(x)=x^2-1, what is m(g o f)(x)?

Mathematics
2 answers:
Andreas93 [3]3 years ago
8 0

Until now, given a function  f(x), you would plug a number or another variable in for x. You could even get fancy and plug in an entire expression for x. For example, given  f(x) = 2x + 3, you could find f(y2 – 1) by plugging y2 – 1 in for x to get f(y2 – 1) = 2(y2 – 1) + 3 = 2y2 – 2 + 3 = 2y2 + 1.

In function composition, you're plugging entire functions in for the x. In other words, you're always getting "fancy". But let's start simple. Instead of dealing with functions as formulas, let's deal with functions as sets of (x, y) points:

Let f = {(–2, 3), (–1, 1), (0, 0), (1, –1), (2, –3)} and  

let g = {(–3, 1), (–1, –2), (0, 2), (2, 2), (3, 1)}.  

 

Find (i) f (1), (ii) g(–1), and (iii) (g o f )(1).

(i) This type of  exercise is meant to emphasize that the (x, y) points are really (x, f (x)) points. To find  f (1), I need to find the (x, y) point in the set of (x, f (x)) points that has a first coordinate of x = 1. Then f (1) is the y-value of that point. In this case, the point with x = 1 is (1, –1), so:

ruslelena [56]3 years ago
5 0

Answer:

gof(x) = x²+8x+15

Step-by-step explanation:

gof(x) = g(f(x))

f(x) = x + 4 and g(x)=x²-1

Substituting

     gof(x) = g(f(x)) = g(x + 4) = (x+4)²-1

       gof(x) = x²+8x+16 -1 = x²+8x+15

That is if f(x) = x + 4 and g(x)=x²-1, gof(x) = x²+8x+15

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The list is known as the sampling frame.

To conduct a survey on current social work majors, a researcher gets a list of all students who have declared a social work major from the registrar from which a sample will be drawn.

This list is known as a sampling frame.

The sampling frame is the list from which units are drawn for the sample.

Hence, the list is known as the sampling frame.

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1 year ago
When will the distance from A to B be negative?
Aneli [31]
The distance from A to B will be negative when the line is trending downward from left to right.
6 0
3 years ago
From 1980 to 1990, the consumer price index (CPI) increased from 82.4 to 130.7. If a gallon of apple juice cost $0.95 in 1980 an
ryzh [129]
Answer: C $1.51

To solve this, start with a proportion. Put the CPI numbers on the left and the apple juice prices on the right.

You will have:

82.4/130.7 = 0.95/x

Cross multiply to solve and you will get the price of the juice is $1.51.
4 0
3 years ago
Read 2 more answers
What procedure will find the sum a+b of two numbers where a and b represent any integer?
ElenaW [278]

Answer:As rational number includes natural number, whole number ,integers  also.

⇒Natural number(1,2,3,4....) is a rational number also.

So, when A= Natural number , B=Any other natural number

Just add two natural number using simple law of addition.

⇒As Whole numbers(0,1,2,3,...) are Rational number also.

So If A=any whole number, B=Any other whole number

Add the whole number in any order using law of addition.

⇒Coming to integers (....-123,....-5,...-1,....12,....59,.....) By taking any two integers ,

1. Both of them are positive add using simple law of addition.

2. One of them is positive and other is negative , if larger one has positive sign before it just subtract smaller one from larger one and put positive sign before the result.and if larger one has negative sign before it ,subtract smaller one from larger one and put negative sign before the result.

⇒If both of them are negative , just add the two integers and apply negative sign before the result.

4. Rational number as fractions ,

A=m/n and B=p/q

A+B=m/n + p/q

find LCM of n and q.

If n and q are co-prime multiply n and q to get the LCM.For example if n=5, q=7, then LCM=5×7=35

If n and q are not co-prime find the factors of n and q .take out the common factors and then multiply the common factors with those factors which are not common.

For example, n=15, q=20

15=5×3

20=2×2×5

common factor=5

non common factor=2,2,3

LCM=5×2×2×3=60

Suppose LCM(n,q)= K

⇒p/q+m/n

=

So ,

which is the way to find LCM of rational number when theyare fractions.

Step-by-step explanation:

4 0
2 years ago
Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.
Vladimir [108]

Answer:

270 yds squared    

Step-by-step explanation:

You need to area of each of the shapes that make up the triangular prism. So, the side triangles, the back rectangle, the bottom rectangle and the top rectangle.

Side triangle (1x): base*height/2

12*5/2

60/2

30 yds, 60 yds for both sides.

Back rectangle: length*width

5*7

35 yds

Bottom Rectangle: length*width

7*12

84 yds

Top rectangle: length*width

7*13

91 yds.

To get the final answer, you add the surface areas together to get the final amount of yards: 30+30+35+84+91= 270 yds squared. Hope this helps.

5 0
2 years ago
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