Question

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

Answer 1

Answer:

$\[3x+\frac{2}{3}\]$

Step-by-step explanation:

$\[f(x)=x-\frac{1}{3}\]$

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

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

But, $\[f(3x+1)=(3x+1)-\frac{1}{3}\]$

Simplifying,

$\[f(3x+1)=3x+(1-\frac{1}{3})\]$

= $\[f(3x+1)=3x+(\frac{3-1}{3})\]$

= $\[f(3x+1)=3x+(\frac{2}{3})\]$

Hence, $\[(f o g)(x)=3x+(\frac{2}{3})\]$