Given
[tex]\begin{gathered} g(x)=2x^2 \\ h(x)=x-3 \end{gathered}[/tex]
To write the expressions of
[tex]\begin{gathered} (h\cdot g)(x) \\ (h+g)(x) \end{gathered}[/tex]
And to evaluate,
[tex](h-g)(-3)[/tex]
Explanation:
It is given that,
[tex]\begin{gathered} g(x)=2x^2 \\ h(x)=x-3 \end{gathered}[/tex]
Then,
[tex]\begin{gathered} (h\cdot g)(x)=h(x)\cdot g(x) \\ =\left(x-3\right)\cdot\left(2x^2\right) \\ =2x^3-6x^2 \end{gathered}[/tex]
Also,
[tex]\begin{gathered} (h+g)(x)=h(x)+g(x) \\ =(x-3)+2x^2 \\ =2x^2+x-3 \end{gathered}[/tex]
And,
[tex]\begin{gathered} (h-g)(-3)=h(-3)-g(-3) \\ =(-3-3)-2(-3)^2 \\ =-6-(2\times9) \\ =-6-18 \\ =-24 \end{gathered}[/tex]
Hence, the answer is,
[tex]\begin{gathered} (h\cdot g)(x)=2x^3-6x^2 \\ (h+g)(x)=2x^2+x-3 \\ (h-g)(-3)=-24 \end{gathered}[/tex]
