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!
Answer:
1/2 i hope i helped
Step-by-step explanation:
Answer:
C. (x-2)^2=7
Step-by-step explanation:
What you have to do first is to get rid of the 3 in the x^2 so you will divide 3 by the whole thing to get x^2-4x=3.
You will then divide -4 by 2 and then square the answer to get 4.
You will then add the 4 into the end of the equation and to the 3 to get x^2-4x+4=7.
You will then make into a perfect square (x-2)^2=7 and that is your answer.
Answer:
180 square inches
Step-by-step explanation:
Area, A is given by A=0.5bh where b is base and h is height. Since both of these dimensions are provided then we substitute the given figures into the formula. Substituting 12 inches for base, b and 30 inches for height, h then the area will be equivalent to
A=0.5*12*30=180 square inches.
Therefore, the area of the described triangle is 180 square inches.
Yo sup??
you can solve this quesion by having the knowledge of trigonometric ratios
let angle B be x, then
tanx=7/3
x=66.8
Hope this helps
