Mark the correct alternative in each of the following:
If g(x) = x2 + x – 2 and 
gof (x) = 2x2 – 5x + 2, then f(x) is equal to
Given that g(x) = x2 + x – 2 and
a. Let f(x) = 2x – 3
gof(x) = g(2x – 3)
⇒ gof(x) = (2x – 3)2 + 2x - 3 – 2
⇒ gof(x) = 4x2 - 12x + 9 + 2x – 5
⇒ gof(x) = 4x2 - 10x + 4
Hence, this option is the required value of f(x).
b. Let f(x) = 2x + 3
gof(x) = g(2x + 3)
⇒ gof(x) = (2x + 3)2 + 2x + 3 – 2
⇒ gof(x) = 4x2 + 12x + 9 + 2x + 1
⇒ gof(x) = 4x2 + 14x + 10
Hence, this option is not the required value of f(x).
c and d option are incorrect because their degree is more than 1. So, the degree of gof will be more than 2.
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