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Let f be the function defined by

f= {(-3,4),(-2,2),(-1,0),(0,1),(1,3),(2,4),(3,-1)}

and let g bed the function defined by

g={(-3,-2),(-2,0),(-1,-4),(0,0),(1,-3),(2,1),(3,2)}

Compute the indicated value if it exists

a. Compute: (f+g)(-3). What does this answer mean in relation to the two functions?

b.Compute: (f-g)(2). Why does it matter which order we subtract the functions? What changes occur if we subtract f from g or (g-f)(2)?

c. Compute: (fg)(-`1). Explain your reasoning in this answer.

d. Compute: (gf)(-3). Does it matter which order we multiply in ?

Sagot :

mhanifa

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

semsee45

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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