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asambeis [7]
3 years ago
10

For which pair of functions is (gºf)(a) =la|-2

Mathematics
1 answer:
nikklg [1K]3 years ago
8 0

Answer:

<h2>              The third</h2>

Step-by-step explanation:

(g\circ f)(x) = g\big(f(x)\big)

so:

I.\quad (g\circ f)(a)=\sqrt{f(a)}=\sqrt{a^2-4}=\sqrt{(a+2)(a-2)}\\\\II.\quad (g\circ f)(a)=2f(a)-2=2(\frac12a-1)-2=a-2-2=a-4\\\\ \bold{III.\quad (g\circ f)(a)=\sqrt{f(a)-5}-2=\sqrt{5+a^2-5}-2=\sqrt{a^2}-2=|a|-2}\\\\ IV.\quad (g\circ f)(a)=4f(a)-5=4(3-3a)-5 = 12-12a-5=-12a+7

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