Question

F(x)= x+1 and g(x)= x^3-1, Find the formula for (fg)(x) and simplify

Answer 1

$fg(x)=x^4+x^3-x-1$

Explanation

Step 1

do the product of the functions:( apply distributive property)

$\begin{gathered} f(x)=x+1 \\ g(x)=x^3-1 \\ so \\ fg(x)=(x+1)(x^3-1) \\ fg(x)=(x\cdot x^3)-(x\cdot1)+(1\cdot x^3)-(1\cdot1) \\ fg(x)=x^{3+1}-x+x^3-1 \\ fg(x)=x^4-x+x^3-1 \\ \text{reordering} \\ fg(x)=x^4+x^3-x-1 \end{gathered}$

so, the answer is

$fg(x)=x^4+x^3-x-1$

I hope this helps you