Final answer:
To find the composition (f⋅g)(x), substitute g(x)=x-5 into f(x)=x^2-3x-10. Expand and simplify to obtain (f⋅g)(x)=x^2 - 13x + 30.
Step-by-step explanation:
To find the composition of functions (f⋅g)(x), where f(x)=x^2-3x-10 and g(x)=x-5, you first need to plug g(x) into f(x). This means that wherever we see an "x" in f(x), we will substitute it with g(x), which is x-5.
Start by writing the function f(x) as f(g(x)):
f(g(x)) = (x-5)^2 - 3*(x-5) - 10
Now, expand and simplify the equation:
f(g(x)) = x^2 - 10x + 25 - 3x + 15 - 10
f(g(x)) = x^2 - 13x + 30
The composition (f⋅g)(x) is therefore x^2 - 13x + 30.