1.

Find f(x), if g(x) = x2 + x – 2 and (gof) (x) = 4x2 – 10x + 4

Answer»

g(x) = x2 + x – 2

(gof) (x) = 4x2 – 10x + 4 

= (2x – 3)2 + (2x – 3) – 2 

= g(2x – 3) = g(f(x)) 

∴ f(x) = 2x – 3 

(gof) (x) = 4x2 – 10x + 4 

= (-2x + 2)2 + (-2x + 2) – 2 

= g(-2x + 2) 

= g(f(x)) 

∴ f(x) = -2x + 2



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