Question

If f(x)=x-1/3 and g(x)=3x+1, what is (f o g)(x)?

Answer 1

`\[3x+(2)/(3)\]`

Explanation:

`\[f(x)=x-(1)/(3)\]`

`\[g(x)=3x+1\]`

Hence,
`\[(f o g)(x)=f(3x+1)\]`

But,
`\[f(3x+1)=(3x+1)-(1)/(3)\]`

Simplifying,

`\[f(3x+1)=3x+(1-(1)/(3))\]`

=
`\[f(3x+1)=3x+((3-1)/(3))\]`

=
`\[f(3x+1)=3x+((2)/(3))\]`

Hence,
`\[(f o g)(x)=3x+((2)/(3))\]`