Answer:
- (h -f)(x) = x² -x +2
- (f +h)(x) = x² +x -2
- (g -f)(x) = x +5
- (g +h)(x) = x² +2x +3
Explanation:
Give three functions f(x), g(x), and h(x), you want various combinations of them.
Operations on functions
If ✧ represents some generic math operator, we often use the notation ...
(f ✧ g)(x)
as a shorthand way to write ...
f(x) ✧ g(x)
The usual meaning of the operator applies.
The three given functions are ...
- f(x) = x -2
- g(x) = 2x +3
- h(x) = x²
(h -f)(x)
The definitions are substituted for the function name:
(h -f)(x) = h(x) -f(x) = x² -(x -2)
(h -f)(x) = x² -x +2
(f +h)(x)
(f +h)(x) = f(x) +h(x) = (x -2) +x²
(f +h)(x) = x² +x -2
(g -f)(x)
(g -f)(x) = g(x) -f(x) = (2x +3) -(x -2) = 2x +3 -x +2
(g -f)(x) = x +5
(g +h)(x)
(g +h)(x) = g(x) +h(x) = (2x +3) +x²
(g +h)(x) = x² +2x +3