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Rainbow [258]
3 years ago
8

If f={ (1,2),(3,5),(4,1)} and g= { (2,3), (5,1),(1,3)} , then (gof)=?

Mathematics
2 answers:
lbvjy [14]3 years ago
6 0

Answer:

a

Step-by-step explanation:

guapka [62]3 years ago
4 0
<h3>Answer: Choice (b)</h3><h3>{ (1, 3),  (3, 1),  (4, 3) }</h3>

==================================================

Work Shown:

The notation "g o f" means g(f(x)). We have f(x) as the inner function that is computed first.

f(x) = {  (1,2),  (3,5), (4,1) }

The x coordinates of each point are: 1, 3, 4

The y coordinates are: 2, 5, 1

So the input x = 1 goes to y = 2 as the output. That output becomes the input of the g(x) function. Using x = 2 as the input for g, we see that 3 is the output. Check out the diagram below to see how each input goes into f, then goes into g to ultimately determine the x,y pairs. So far we've shown that x = 1 ultimately leads to y = 3.

Let's do another input: if x = 3 is plugged into f(x), then the output is 5 because of the point (3,5). Then x = 5 is plugged into g(x) to get x = 5 lead to y = 1. Ultimately x = 3 leads to y = 1 giving us (3,1) as another point.

Lastly, if x = 4 is plugged into f we get y = 1 as an output, which in turn is plugged into g to get 3 as the final output. The point (4,3) is the last ordered pair.

Again there's a lot to keep track of, so it helps to have a diagram as shown below.

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Juan ordered 20 pizzas for a party. 45% of the pizzas have 8 slices each. The remaining 55% of the pizzas have 12 slices each. C
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Total number of pizzas Juan ordered 20

Since, 45\% of pizzas have 8 slices.

Therefore, number of pizzas with 8 slices are: 45\%\times(20)

                                                                                          =\frac{45}{100} \times(20)

                                                                                          =\frac{45}{10} \times(2)

                                                                                          =\frac{90}{10}

                                                                                          =9 pizzas


Also, since, 55\% of pizzas have 12 slices.

Therefore, number of pizzas with 12 slices are: 55\%\times(20)

                                                                                          =\frac{55}{100} \times(20)

                                                                                          =\frac{55}{10} \times(2)

                                                                                          =\frac{110}{10}

                                                                                          =11 pizzas


Now, there are 9 pizzas with 8 slices and 11 pizzas with 12 slices.

Therefore, total number of slices of pizza are: =(9)(8)+(11)(12)

                                                                            =72+132

                                                                            =204 slices

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