Q1 of 215 Page 2

Find gof and fog when f: R → R and g: R → R is defined by

f(x) = 2x + x2 and g(x) = x3

Since, f:R → R and g:R → R


fog:R → R and gof:R → R


f(x) = 2x + x2 and g(x)=x3


Now, gof(x) = g(f (x)) =g(2x + x2)


gof (x)=(2x + x2)3 = x6 + 8x3 + 6x5 + 12x4


and fog(x)=f(g(x))= f(x3)


⇒ fog(x) = 2x3 + x6


So, gof(x) = x6 + 6x5 + 12x4 + 8x3 and fog(x) = 2x3 + x6


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