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

Question

Philoid · Accepted 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