Chapter SH, Problem 9.31EP

To determine

To state the result of the combination

Answer to Problem 9.31EP

  $(f\times g)(x)=2x^3+x^2+2x+3$

Explanation of Solution

Given information :

Functions provided are:- $f(x)=2x^2-x+3$ and $g(x)=x+1$

There are several ways that two or more functions can be combined to form new functions.

Addition of two functions $f(x)$ and $g(x)$ ;

  $(f+g)(x)=f(x)+g(x)$

Subtraction of two functions $f(x)$ and $g(x)$ ;

  $(f-g)(x)=f(x)-g(x)$

Multiplication of two functions $f(x)$ and $g(x)$ ;

  $(f\times g)(x)=f(x)\times g(x)$

Divison of two functions $f(x)$ and $g(x)$ ;

  $(f÷g)(x)=\frac{f(x)}{g(x)}$

Here,

  $(f\times g)(x)=f(x)\times g(x)$

Substituting the values.

  $(f\times g)(x)=(2x^2-x+3)\times (x+1)$

Multiplying.

  $(f\times g)(x)=2x^3-x^2+3x+2x^2-x+3$

Simplifying.

  $(f\times g)(x)=2x^3+x^2+2x+3$