Math Problem Statement

Suppose f(-3) = 7 and g(-3) = -2.

  1. (f- g) (-3) =
  2. (fg)(-3) = 3.(g/f)(-3)
  3. (f/g) (-3)= Submit Question A decimal is not an acceptable answer. A decimal is not an acceptable answer.

Solution

Given the values f(3)=7f(-3) = 7 and g(3)=2g(-3) = -2, let's solve the following expressions:

1. (fg)(3)=f(3)g(3)(f - g)(-3) = f(-3) - g(-3)

(fg)(3)=7(2)=7+2=9(f - g)(-3) = 7 - (-2) = 7 + 2 = 9

2. (fg)(3)=f(3)g(3)(fg)(-3) = f(-3) \cdot g(-3)

(fg)(3)=7(2)=14(fg)(-3) = 7 \cdot (-2) = -14

3. (gf)(3)=g(3)f(3)\left(\frac{g}{f}\right)(-3) = \frac{g(-3)}{f(-3)}

(gf)(3)=27\left(\frac{g}{f}\right)(-3) = \frac{-2}{7}

4. (fg)(3)=f(3)g(3)\left(\frac{f}{g}\right)(-3) = \frac{f(-3)}{g(-3)}

(fg)(3)=72=72\left(\frac{f}{g}\right)(-3) = \frac{7}{-2} = -\frac{7}{2}

Summary of answers:

  1. (fg)(3)=9(f - g)(-3) = 9
  2. (fg)(3)=14(fg)(-3) = -14
  3. (gf)(3)=27\left(\frac{g}{f}\right)(-3) = \frac{-2}{7}
  4. (fg)(3)=72\left(\frac{f}{g}\right)(-3) = -\frac{7}{2}

Would you like more details on any step?

Here are five related questions to explore further:

  1. What is f(x)g(x)f(x) - g(x) for any value of xx?
  2. How do you calculate the product of two functions f(x)f(x) and g(x)g(x)?
  3. How would you interpret the quotient of two functions graphically?
  4. Can you express (fg)(x)(fg)(x) in terms of function compositions?
  5. What are the conditions when the division of two functions is undefined?

Tip: When dividing two functions, always check if the denominator function is zero at the point you're evaluating to avoid undefined results.

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Math Problem Analysis

Mathematical Concepts

Function Operations
Algebra

Formulas

(f - g)(x) = f(x) - g(x)
(fg)(x) = f(x) * g(x)
(g/f)(x) = g(x) / f(x)
(f/g)(x) = f(x) / g(x)

Theorems

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Suitable Grade Level

Grades 9-11