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Sagot :
Answer:
- See below
Step-by-step explanation:
a) Sum of two functions
- f(-3) = 4, g(-3) = - 2 (from given sets of data)
- (f + g)(-3) = f(-3) + g(-3) = 4 + (-2) = 2
b) Difference of two functions
- f(2) = 4, g(2) = 1 (from given sets of data)
- (f - g)(2) = f(2) - g(2) = 4 - 1 = 3
c) Product of two functions
- f(-1) = 0, g(-1) = - 4 (from given sets of data)
- (fg)(- 1) = f(-1)*g(-1) = 0*(-4) = 0
d) Product of functions, fg = gf, same result with different order
- g(-3) = -2, f(-3) = 4 (from given sets of data)
- (gf)(- 3) = (-2)*4 = - 8
Answer:
(a) (f + g)(-3) = 2
(b) (f - g)(2) = 3
(c) (fg)(-1) = 0
(d) (gf)(-3) = -8
Step-by-step explanation:
Function operations
(f + g)(x) = f(x) + g(x)
(f - g)(x) = f(x) - g(x)
(f · g)(x) = f(x) · g(x)
Question (a)
From the given data sets:
- f(-3) = 4
- g(-3) = -2
⇒ (f + g)(-3) = f(-3) + g(-3) = 4 + -2 = 4 - 2 = 2
Question (b)
From the given data sets:
- f(2) = 4
- g(2) = 1
⇒ (f - g)(2) = f(2) - g(2) = 4 - 1 = 3
(g - f)(2) = g(2) - f(2) = 1 - 4 = -3
The change that occurs between (f - g)(2) and (g - f)(2) is that one is the negative of the other.
Question (c)
From the given data sets:
- f(-1) = 0
- g(-1) = -4
⇒ (fg)(-1) = f(-1) · g(-1) = 0 · -4 = 0
Question (d)
From the given data sets:
- f(-3) = 4
- g(-3) = -2
⇒ (gf)(-3) = g(-3) · f(-3) = -2 · 4 = -8
If we change the order in which we multiply the functions, the answer doesn't change:
(fg)(-3) = f(-3) · g(-3) = 4 · -2 = -8
So it doesn't matter in which order we multiply.
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