Find gof and fog when f: R → R and g: R → R is defined by f(x) = 2x + x 2 and g(x) = x 3

Question

Philoid · Accepted Answer

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