[tex]f(x)-g(x)=x^2\text{ - 2x + 6}[/tex]Explanation:[tex]\begin{gathered} \text{Given:} \\ f(x)=x^2\text{ + 1} \\ g(x)\text{ = }2x\text{ - 5} \end{gathered}[/tex]
We are to find f(x) - g(x):
We will subtract the expressions of g(x) from f(x)
[tex]\begin{gathered} f(x)-g(x)=x^2\text{ + 1 - (2x - 5)} \\ \end{gathered}[/tex]
Expanding the parenthesis using distributive property:
[tex]\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}[/tex]
collect like terms:
[tex]\begin{gathered} f(x)-g(x)=x^2\text{ -2x + 5 }+\text{ 1} \\ f(x)-g(x)=x^2\text{ - 2x + 6} \end{gathered}[/tex]
