Answer:
0
Step-by-step explanation:
Solution:-
We are given two functions as follows:
[tex]f ( x ) = x^2 - 15\\\\g ( x ) = 2x[/tex]
We need to determine the composite function defined as ( g - f ) ( x ). To determine this function we need to make sure that both function exist for all real positive value of x.
The function f ( x ) is a quadratic function which has real values for all values of x. Similarly, function g ( x ) is a linear line that starts from the origin. Hence, both functions are defined over the domain ( -∞, ∞ )
We will perform arithmetic operation of subtracting function f ( x ) from g ( x ) as follows:
[tex][ g - f ] ( x ) = g ( x ) - f ( x )\\\\\\( g - f ) ( x ) = x^2 - 15 - 2x\\\\[/tex]
Now evaluate the above determined function at x = -3 as follows:
[tex]( g - f ) ( -3 ) = ( -3 )^2 - 2 ( -3 ) - 15\\\\( g - f ) ( -3 ) = 9 + 6 - 15\\\\( g - f ) ( -3 ) = 0[/tex]