9514 1404 393
Answer:
2*(3*4) = 41/16
Step-by-step explanation:
Your function is not carefully defined.* We assume you intend ...
f(a, b) = (2a +3b)/(a +b)
and you want to find ...
f(2, f(3, 4))
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Filling in the values and doing the arithmetic, we have ...
[tex]2*(3*4)=\dfrac{2\cdot2+3\cdot\dfrac{2\cdot3+3\cdot4}{3+4}}{2+\dfrac{2\cdot3+3\cdot4}{3+4}}=\dfrac{4+3\cdot\dfrac{18}{7}}{2+\dfrac{18}{7}}\\\\=\dfrac{4\cdot7+3\cdot18}{2\cdot7+18}=\dfrac{82}{32}=\boxed{\dfrac{41}{16}}[/tex]
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* We have assumed that the definition is describing the result of using the infix operator * in an expression of the form a*b. We have also assumed that your use of the ÷ symbol means ...
a*b ≡ (2a+3b)/(a+b)
as opposed to the strict Order of Operations interpretation ...
a*b ≡ 2a + (3b/a) +b
