Question

Suppose that the functions g and h are defined for all real numbers x as follows. 9g(x) = 2x ^ 2 h(x) = x - 3Write the expressions for (hg)(x) and (h + g)(x) and evaluate (h - g)(- 3) .

Answer 1

Given

`\begin{gathered} g(x)=2x^2 \\ h(x)=x-3 \end{gathered}`

To write the expressions of

`\begin{gathered} (h\cdot g)(x) \\ (h+g)(x) \end{gathered}`

And to evaluate,

`(h-g)(-3)`

Step-by-step explanation:

It is given that,

`\begin{gathered} g(x)=2x^2 \\ h(x)=x-3 \end{gathered}`

Then,

`\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}`

Also,

`\begin{gathered} (h+g)(x)=h(x)+g(x) \\ =(x-3)+2x^2 \\ =2x^2+x-3 \end{gathered}`

And,

`\begin{gathered} (h-g)(-3)=h(-3)-g(-3) \\ =(-3-3)-2(-3)^2 \\ =-6-(2*9) \\ =-6-18 \\ =-24 \end{gathered}`

Hence, the answer is,

`\begin{gathered} (h\cdot g)(x)=2x^3-6x^2 \\ (h+g)(x)=2x^2+x-3 \\ (h-g)(-3)=-24 \end{gathered}`