ExplanationTo answer the question, “If \(\alpha (x)= 2x^2 + 2\), which of the following is equal to \(\alpha (x)\)?” plug 4 into the given function.
\(\alpha (4)= 2(4)^2 + 2\)
\(\alpha (4)= 34\)
Do not fall for trap answer choice (E). The correct answer is 34, which does not appear in the choices in that form. Trap choice (E) is \(\alpha (34)\) , which equals \(2(34)^2 + 2\); this is much greater than 34.
Instead, solve each answer choice until one equals 34. Choice (A), \(\alpha (\alpha (-1))\), uses the function symbol twice, so plug –1 into the function, then plug the resulting answer back into the function again:
\(\alpha(-1)= 2(–1)^2 + 2 = 4\)
\(\alpha(4)= 2(4)^2 + 2 = 34\)
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