Question

Let h(x) = 2x^2 + x - 5 and g(x) = -3x^2 + 4x + 1.

Answer 1

`\begin{gathered} h(x)+g(x)=-x^2\text{ + 5x - 4} \\ h(x)-g(x)=5x^2\text{ - 3x - 6} \end{gathered}`

Step-by-step explanation

We have the two functions:

`\begin{gathered} h(x)=2x^2\text{ + x - 5} \\ g(x)=-3x^2\text{ + 4x + 1} \end{gathered}`

a. To find h(x) + g(x), we have to add the two functions together.

That is:

`\begin{gathered} h(x)+g(x)=2x^2+x-5+(-3x^2\text{ + 4x + 1)} \\ Expand\text{ the bracket and collect like terms:} \\ h(x)+g(x)=2x^2+x-5-3x^2+\text{ 4x + 1} \\ h(x)+g(x)=2x^2-3x^2\text{ + x + 4x - 5 + 1} \\ h(x)+g(x)=-x^2\text{ + 5x - 4} \end{gathered}`

b. To find h(x) - g(x), we have to subtract g(x) from h(x).

That is:

`\begin{gathered} h(x)-g(x)=2x^2+x-5-(-3x^2\text{ + 4x + 1)} \\ h(x)\text{ - g(x) = }2x^2+x-5+3x^2\text{ - 4x - 1} \\ h(x)-g(x)=2x^2+3x^2\text{ + x - 4x - 5 - 1} \\ h(x)-g(x)=5x^2\text{ - 3x - 6} \end{gathered}`