Keywords:
Functions, subtraction, operation of functions
For this case, we are given two functions of the form \(y_ {1} = f (x)\), where \(f (x) = 4x + 1\) and\(y_ {2} = g (x)\), where \(g (x) = x ^ 2-5\). We must find the subtraction (f-g) (x). So, by definition of operation of functions we have to:
\((f-g) (x) = f (x) -g (x)\)
So, we have:
\((f-g) (x) = 4x + 1- (x ^ 2-5)\)
Knowing that: \(- * + = -\ and\ - * - = +\)
\((f-g) (x) = 4x + 1-x ^ 2 + 5\\(f-g) (x) = - x ^ 2 + 4x + 6\)
Answer:
\((f-g) (x)\)is given by\(-x ^ 2 + 4x + 6\)
