Q. 1 A

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

f(x) = 2x + 3 and g(x) = x^{2} + 5

Answer :

Since, f:R → R and g:R → R

fog:R → R and gof:R → R

Now, f(x) = 2x + 3 and g(x) = x^{2} + 5

gof(x) = g(2x + 3) = (2x + 3)^{2} + 5

⇒ gof(x) = 4x^{2} + 12x + 9 + 5 = 4x^{2} + 12x + 14

fog (x) = f(g(x)) = f (x^{2} + 5) = 2 (x^{2} + 5) + 3

⇒ fog(x)= 2x^{2} + 10 + 3 = 2x^{2} + 13

Hence, gof(x) = 4x^{2} + 12x + 14 and fog (x) = 2x^{2} + 13

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