Is it true or false that the middle term of a perfect square trinomial is equal to 2 × √(first term) × √(last term)?

Mathematics

1 answer:

FinnZ [79.3K]2 years ago

3 0

False, because it's equal to 2 × first term × last term

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Given the tables for f & g below, find the following: x f ( x ) g ( x ) 0 9 7 1 4 8 2 3 6 3 5 1 4 7 5 5 1 2 6 6 0 7 0 4 8 2

d1i1m1o1n [39]

$\\(i)\\
\text{We know that the average rate of change of a function f(x) on inerval [a,b] is}\\
\\
f_{avg}=\frac{f(b)-f(a)}{b-a}\\
\\
\text{so using this the average rate of chang of g for x on interval }[3,7] \text{ is}\\
\\
g_{avg}=\frac{g(7)-g(3)}{7-3}\\
\\
=\frac{4-1}{4}\\
\\
=\frac{3}{4}\\
\\
\text{so average rate of change of g on interval [3,7] is }\frac{3}{4}$

$\\(ii)\\ \text{Average rate of chang of f for x on interval }[3,7] \text{ is}\\
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f_{avg}=\frac{f(7)-f(3)}{7-3}\\
\\
=\frac{0-5}{4}\\
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=\frac{-5}{4}\\
\\
\text{so average rate of change of g on interval [3,7] is }\frac{-5}{4}$

$\\(iii)\\
\text{Since g(4)=5, so we have}\\
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f(g(4))=f(5)\\
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\text{since the value of f is 1 at x=5. so }\\
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f(g(4))=f(5)=1\\
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\text{hence we have, }f(g(4))=$ 1

$\\(iv)\\
\text{Since f(3)=5, so we have}\\
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g(f(3))=g(5)\\
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\text{since the value of g is 2 at x=5. so }\\
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g(f(3))=g(5)=2\\
\\
\text{hence we have, }g(f(3))=$ 2