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klemol [59]
3 years ago
13

If f(x) = 2x + 3 and g(x) = (x - 3)/2, what is the value of f[g(-5)]?

Mathematics
1 answer:
kap26 [50]3 years ago
3 0
<span>If f(x) = 2x + 3 and g(x) = (x - 3)/2, what is the value of f[g(-5)]? f[g(-5)] means substitute -5 for x in the right side of g(x), simplify, then substitute what you get for x in the right side of f(x), then simplify. It's a "double substitution". To find f[g(-5)], work it from the inside out. In f[g(-5)], do only the inside part first. In this case the inside part if the red part g(-5) g(-5) means to substitute -5 for x in g(x) = (x - 3)/2 So we take out the x's and we have g( ) = ( - 3)/2 Now we put -5's where we took out the x's, and we now have g(-5) = (-5 - 3)/2 Then we simplify: g(-5) = (-8)/2 g(-5) = -4 Now we have the g(-5)] f[g(-5)] means to substitute g(-5) for x in f[x] = 2x + 3 So we take out the x's and we have f[ ] = 2[ ] + 3 Now we put g(-5)'s where we took out the x's, and we now have f[g(-5)] = 2[g(-5)] + 3 But we have now found that g(-5) = -4, we can put that in place of the g(-5)'s and we get f[g(-5)] = f[-4] But then f(-4) means to substitute -4 for x in f(x) = 2x + 3 so f(-4) = 2(-4) + 3 then we simplify f(-4) = -8 + 3 f(-4) = -5 So f[g(-5)] = f(-4) = -5</span>
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Step-by-step explanation:

It is given that the points M, N, and P are the midpoints of sides AC, BC and AB respectively. It means AC, BC and AB are median of the triangle ABC.

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Since MN, NP and MP are midsegments of the triangle, therefore the length of these sides are half of AB, AC and BC respectively. In triangle ABC and MNP corresponding side are proportional.

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By the property of similar triangles,

\frac{\text{Area of }\triangle MNP}{\text{Area of }\triangle ABC}=\frac{PM^2}{BC^2}

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\frac{\text{Area of }\triangle MNP}{\text{Area of }\triangle ABC}=\frac{1}{4}

Hence proved.

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