If \(\alpha(x)= 2x^2 + 2\), which of the following is equal to \(\alpha(4)\) ?
Now since GRE tests your ability to exploit opportunities provided to solve the problem in minimum amount of time, I won't calculate the value of \(\alpha(4)\) and compare it with the value each of the choices yields. Instead I am going to try and see which of the functions given in the choices can be reduced to \(\alpha(4)\), given that two such ready made candidates exist.
(A) \(\alpha(\alpha(-1))\)
(C) \(\alpha(\alpha(2))\)
I will first check with Choice C - \(\alpha(\alpha(2))\) - since I am more comfortable with positive numbers. Now \(\alpha(2) = 2(2)^2 + 2 = 10\) and this reduces the expression to \(\alpha(10)\). But his not the same as \(\alpha(4)\). So we reject this choice.
Let us now try \(\alpha(\alpha(-1))\). Resolving the innermost function first, we get \(\alpha(-1) = 2(-1)^2 + 2 = 2 + 2 = 4\). This reduces the expression to \(\alpha(4)\). Thus Choice A is equal to \(\alpha(4)\) and is the correct answer choice.
If I had decided to proceed from the first choice, \(\alpha(\alpha(-1))\), I would have gotten to the answer in even shorter time.
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