Given f(x) = x^2 + 1 and g(x) = x-2
a. Find (f-g)(-2)
[f-g](x) = f(x) - g(x) = x^2-x+3
[f-g](-2) = (-2)^2-(-2)+3 = 9
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b. Find f[g(5)]
f[g(5)] = f[5-2] = f[3] = 9+1 = 10
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problem a.
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(f-g)(x) = f(x) - g(x)
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(f-g)(-2) = f(-2) - g(-2)
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f(x) = x^2 + 1
f(-2) = (-2)^2 + 1
f(-2) = 4+1
f(-2) = 5
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g(x) = x-2
g(-2) = -2-2
g(-2) = -4
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f-g(-2) = f(-2) - g(-2) = 5 - (-4) = 5 + 4 = 9
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answer for a is:
f-g(-2) = 9
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problem b.
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g(x) = x-2
g(5) = 5-2
g(5) = 3
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f(x) = x^2 + 1
f(g(5)) = (g(5))^2 + 1
since g(5) = 3, equation becomes:
f(g(5)) = 3^2 + 1
f(g(5)) = 9 + 1 = 10
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answer for b is:
f(g(5)) = 10
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in general, you substitute whatever value is replacing x in the equation to get your answers.
looking at problem b in this way, we would get a general solution as follows:
f(x) = x^2 + 1
g(x) = x-2
substitute g(x) for x:
f(g(x)) = (g(x))^2 + 1
substitute the equation for g(x) on the right hand side.
f(g(x)) = (x-2)^2 + 1
remove parentheses:
f(g(x)) = x^2 - 4*x + 4 + 1
simplify:
f(g(x)) = x^2 - 4*x + 5
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substituting 5 for x:
f(g(5)) = (5^2 - 4*5 + 5
simplifying:
f(g(5)) = 25 - 20 + 5
f(g(5)) = 10
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answer is the same as above where we first solved for g(5) which became 3, and then substituted that value in f(g(x)) which made it f(3)).
Hope this helps!
The y-intercept of linear function (f- g)(x) is (0,9)
<h3>How to determine the y-intercept?</h3>
The table of values is given as:
x -6 -4 -1 3 4
f(x) 15 11 5 -3 -5
g(x) -36 -26 -11 9 14
The equations of the functions is calculated using:
So, we have:
Evaluate
f(x) = -2x + 3
Also, we have:
Evaluate
g(x) = 5x - 6
Next, we calculate (f - g)(x) using:
(f - g)(x) = f(x) - g(x)
This gives
(f - g)(x) = -2x + 3 - 5x + 6
Substitute 0 for x
(f - g)(0) = -2(0) + 3 - 5(0) + 6
Evaluate
(f - g)(0) = 9
Hence, the y-intercept of (f- g)(x) is (0,9)
Read more about linear functions at:
brainly.com/question/24896196
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Answer:
D
Step-by-step explanation:
I think the intervals can pretty much be infinite.
Answer:
Step-by-step explanation:
12.718 units
Step-by-step explanation:
The coordinates of the vertices of parallelogram WXYZ are given to be W(0,-1), X(4,0), Y(3,-2) and Z(-1,-3).
So, the perimeter of the parallelogram will be 2(WX + XY) {Since opposite sides of parallelogram are same in length}
Now, length of WX = units, To find the units click this link :
https://tex.z-dn.net/?f=%5Csqrt%7B(-1)%5E%7B2%7D%20%2B%204%5E%7B2%7D%20%7D%20%3D%20%5Csqrt%7B17%7D%20%3D%204.123
And, length of XY = units, To find the units click this link :
https://tex.z-dn.net/?f=%5Csqrt%7B(4-3)%5E%7B2%7D%20%2B%20(0-(-2))%5E%7B2%7D%7D%20%3D%20%5Csqrt%7B5%7D%20%3D%202.236
Therefore, the perimeter of the parallelogram WXYZ = 2(4.123 + 2.236) = 12.718 units. (Answer)
