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algebra intermediate

Problem

Let

f

be the function defined by

f (x) = a x^{2} - 2

for some positive

a

. If

f (f (2)) = - 2

then

a =

(A)

f r a c (2 - s q r t (2), 2)

(B)

1/2

(C)

2 - s q r t (2)

(D)

s q r t (2) /2

Solution

If

f (x) = - 2

, then

a x^{2} = 0 ⟹ x = 0

. Therefore

f (2) = 0 ⟹ 2 a = 2

, so

\frac{2}{2}

Final answer

D