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If g(x) = x2 + x – 1 and (gof)(x) = 4x2 – 10x + 5, then f(54) is equal to

  1. −32
  2. −12
  3. 12
  4. 32

Answer (Detailed Solution Below)

Option 2 : −12

Detailed Solution

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Explanation -

g(x) = x2 + x – 1

gof(x) = 4x2 – 10x + 5

g(f(x) = 4x2 – 10x + 5

f2(x) + f(x) – 1 = 4x2 – 10x + 5

Putting x = 5/4 and f(5/4) = t

t2+t+14=0

t = -1/2 or f(5/4) = -1/2

Hence Option (2) is correct.

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