The results of subtraction of functions are listed below:
- x - 8
- m(x) = x² + 10 · x + 5
- m(3) = 44
How to use the subtract function operator
There three fundamental binary operators (addition, multiplication, composition) and two secondary binary operators (subtraction, division) for functions. The subtraction is operation derived from addition, defined by the following expression:
(h - f) (x) = h(x) - f(x) (1)
Now we proceed to develop each expression:
i) (h - f) (x):
- h(x) = 2 · x - 3, f(x) = x + 5 Given
- (h - f)(x) = (2 · x - 3) - (x + 5) Definition of subtraction between functions
- (2 · x - x) + [(- 3) + (- 5)] Associative and commutative properties / (- 1) · a = - a
- x - 8 Distributive property / Definitions of addition and subtraction / Result
ii) m(x) = (g - j) (x):
- g(x) = x² + 6 · x + 5, j(x) = - 4 · x Given
- m(x) = (x² + 6 · x + 5) - (- 4 · x) Definition of subtraction between functions
- m(x) = x² + (6 · x + 4 · x) + 5 Associative, commutative and distributive property / (- a) · (- b) = a · b
- m(x) = x² + 10 · x + 5 Distributive property / Definition of adition / Result
iii) m(3):
m(3) = 3² + 10 · 3 + 5
m(3) = 9 + 30 + 5
m(3) = 44
To learn more on subtraction of functions: https://brainly.com/question/14630324
#SPJ1
