Please help me by answering the below question as I have a Grade 12 Pre Calc test in 2 hours and do not have the answer sheet for the practice test I was given, Will still give best answer to the person who best describes how to do this problem.
Consider the following table of values
(x) 0 1 2 3 4 5 6
f(x) 0 2 4 6 8 10 12
g(x) 7 6 5 4 3 2 1
Question 1: Explain how to determine the result of. f(g(2) )Then evaluate the expression by referring to the table of values.
Question 1b: Is it possible to evaluate G(f(5))? Justify your answer using references to the range of f and the domain of g.
In General Given f(x) and g(x) does f(g(x)) equal g(f(x))? Give an example to support your answer.
Consider the following table of values
(x) 0 1 2 3 4 5 6
f(x) 0 2 4 6 8 10 12
g(x) 7 6 5 4 3 2 1
Question 1: Explain how to determine the result of. f(g(2) )Then evaluate the expression by referring to the table of values.
Question 1b: Is it possible to evaluate G(f(5))? Justify your answer using references to the range of f and the domain of g.
In General Given f(x) and g(x) does f(g(x)) equal g(f(x))? Give an example to support your answer.
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I, for one, would first figure out the general equations for f(x) and g(x). This is NOT ABSOLUTELY NECESSARY, so if you do not understand it or are not interested, you can jump to the part where I solve your questions. :-)
Let us start with f(x). Let us pick the coordinates of two random points: e.g. (0,0) and (1,2). We use the following formula to find the equation starting with two points:
f(x) = ((y2 - y1)/(x2 - x1))(x - x1) + y1
Filling in our two points (0,0) and (1,2), we get:
f(x) = ((2 - 0)/(1 - 0))(x - 0) + 0 = 2x
Thus, the equation for our first function is f(x) = 2x
We do the same for g(x), using the equations (0,7) and (1,6):
g(x) = ((6 - 7)/(1 - 0))(x - 0) + 7 = -x + 7
Thus, the equation for our second function is g(x) = -x + 7
Now we can start answering your questions:
1) First you need to determine g(2). Then you fill in your solution, let's call it x, in f(x):
f(g(2)) = f(5) = 10
1b) Well, first we calculate f(5), which is 10. As you can see in your table, 10 is not a value of x that we may fill in, thus, out of the domain of g.
2) No, you can use x = 1 as an example
f(g(1)) = f(6) = 12
g(f(1)) = g(2) = 5
So, as you can see, f(g(x)) does not equal g(f(x)).
I hope this helped you! Free feel to send me an e-mail if you don't understand it yet.
Let us start with f(x). Let us pick the coordinates of two random points: e.g. (0,0) and (1,2). We use the following formula to find the equation starting with two points:
f(x) = ((y2 - y1)/(x2 - x1))(x - x1) + y1
Filling in our two points (0,0) and (1,2), we get:
f(x) = ((2 - 0)/(1 - 0))(x - 0) + 0 = 2x
Thus, the equation for our first function is f(x) = 2x
We do the same for g(x), using the equations (0,7) and (1,6):
g(x) = ((6 - 7)/(1 - 0))(x - 0) + 7 = -x + 7
Thus, the equation for our second function is g(x) = -x + 7
Now we can start answering your questions:
1) First you need to determine g(2). Then you fill in your solution, let's call it x, in f(x):
f(g(2)) = f(5) = 10
1b) Well, first we calculate f(5), which is 10. As you can see in your table, 10 is not a value of x that we may fill in, thus, out of the domain of g.
2) No, you can use x = 1 as an example
f(g(1)) = f(6) = 12
g(f(1)) = g(2) = 5
So, as you can see, f(g(x)) does not equal g(f(x)).
I hope this helped you! Free feel to send me an e-mail if you don't understand it yet.