Answer:
[tex](f-g)(x)= x^2-4x-5[/tex]
Step-by-step explanation:
We have the two functions:
[tex]f(x)=x^2-3x-10\text{ and } g(x)=x-5[/tex]
And we want to find (f-g)(x).
(f-g)(x) is equivalent to f(x)-g(x).
Therefore:
[tex]\begin{aligned} (f-g)(x)&=f(x)-g(x)\\ &=(x^2-3x-10)-(x-5)\end{aligned}[/tex]
Simplify:
[tex]\begin{aligned} &=x^2-3x-10-x+5 \\ &=(x^2)+(-3x-x)+(-10+5) \\ &=x^2-4x-5\end{aligned}[/tex]
Therefore:
[tex](f-g)(x)= x^2-4x-5[/tex]
