Answer :

Since, f:R R and g:R R


fog:R R and gof:R R


Now, f(x) = 2x + 3 and g(x) = x2 + 5


gof(x) = g(2x + 3) = (2x + 3)2 + 5


gof(x) = 4x2 + 12x + 9 + 5 = 4x2 + 12x + 14


fog (x) = f(g(x)) = f (x2 + 5) = 2 (x2 + 5) + 3


fog(x)= 2x2 + 10 + 3 = 2x2 + 13


Hence, gof(x) = 4x2 + 12x + 14 and fog (x) = 2x2 + 13


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