Chapter 1.2, Problem 2GCE

To determine

To find: $Y_3$ and use table to observe the result for definition of $Y_3$ .

Answer to Problem 2GCE

  $6x^2+x-2$

Explanation of Solution

Given information:

  $\begin{array}{l}{Y}_1=f\left(x\right)=2x-1\\ Y_2=f\left(x\right)=3x+2\\ Y_3=Y_1\cdot Y_2\end{array}$

From the table, $\left(f\cdot g\right)\left(x\right)=f\left(x\right)\cdot g\left(x\right)$

Calculation:

Let’s substitute the value of $Y_1\text{ and }{Y}_2$ in the equation for $Y_3$ and simplify as follows:

  $\begin{array}{c}{Y}_3=Y_1\cdot Y_2\\ =\left(2x-1\right)\cdot \left(3x+2\right)\\ =6x^2-3x+4x-2\\ =6x^2+x-2\end{array}$

Thus, the value of $Y_3$ is $6x^2+x-2$ .