Question

I really am struggling with this, could I have some help?

Answer 1

`f(x)-g(x)=x^2\text{ - 2x + 6}`Step-by-step explanation:
`\begin{gathered} \text{Given:} \\ f(x)=x^2\text{ + 1} \\ g(x)\text{ = }2x\text{ - 5} \end{gathered}`

We are to find f(x) - g(x):

We will subtract the expressions of g(x) from f(x)

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

Expanding the parenthesis using distributive property:

`\begin{gathered} f(x)-g(x)=x^2\text{ + 1 - (2x) -(-5)} \\ mu\text{ltiplication of same signs gives positive sign} \\ m\text{ ultiplication of opposite signs give negative sign} \\ \\ f(x)-g(x)=x^2\text{ + 1 -2x + 5} \end{gathered}`

collect like terms:

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