Question

If `f(x) =x+2`and `g(x)=x^2 +3`, what is `(f@g)(x)`?

Answer 1

`(f@g)(x)=x^2+5`

Explanation:

`D_f=RR`
`D_g=RR`

`D_(f@g)={AAx` `inRR` `:x` `inD_g` `,g(x)inD_f` `}` `=`

`={x` `inRR, x^2+3inRR}` `=RR`

• For `x` `inD_(f@g)=RR`,

`(f@g)(x)=f(g(x))=f(x^2+3)=x^2+3+2=x^2+5`