What are the domain and range of the function mc013-1
1 answer:
The domain and range of the function are:
<h3>How to determine the domain of the function?</h3>In this exercise, you're given the following function f(x) = 5ˣ ⁻ ³ + 1. Next, we would equate the function to zero (0) to determine its domain as follows:
0 = 5ˣ ⁻ ³ + 1.
-1 = 5ˣ ⁻ ³
-(5⁰) = 5ˣ ⁻ ³
-0 = x - 3
x = 3.
Therefore, the domain are all real numbers and they can be substituted for x to return a valid f(x) value.
From the graph of the given function (5ˣ ⁻ ³ + 1), we can logically deduce that the range comprises all real numbers that are greater than 1.
Read more on domain here: brainly.com/question/17003159
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Part (i)
We have 60 students total, and 5 didn't like any of the two subjects, so that must mean 60-5 = 55 students liked at least one subject.
<h3>Answer: 55</h3>=========================================================
Part (ii)
We have 15 who like math only, 20 who like science only, and 55 who like either (or both). Let x be the number of people who like both classes.
We can then say
15+20+x = 55
x+35 = 55
x = 55-35
x = 20
This means 20 people liked both subjects
<h3>Answer: 20</h3>=========================================================
Part (iii)
There are 15 people who like math only, and 20 who like both. Therefore, there are 15+20 = 35 people who like math (and some of these people also like science)
<h3>Answer: 35</h3>=========================================================
Part (iv)
We'll follow the same idea as the previous part. There are 20 people who like science only and 20 who like both subjects. That yields 40 people total who like science (and some of these people also like math).
<h3>Answer: 40</h3>=========================================================
Part (v)
We'll draw a rectangle to represent the entire group of 60 students. This is considered the universal set. Inside the rectangle will be two overlapping circles to represent math (M) and science (S).
We'll have 15 go in circle M, but outside circle S to represent the 15 people who like math only. Then we have 20 go in circle S but outside circle M to show the 20 people who like science only. We have another copy of 20 go in the overlapped region between the circles. This is the 20 people who like both classes. And finally, we have 5 go outside both circles, but inside the rectangle. These are the 5 people who don't like either subject.
Note how all of the values in the diagram add up to 60
15+20+20+5 = 60
This helps confirm we have the correct values.
<h3>Answer: See the venn diagram below</h3>