Math Problem Statement

Now (b) Find (f − g)(0).

Solution

To find (fg)(0)(f - g)(0), you need to evaluate the difference between the functions f(x)f(x) and g(x)g(x) at x=0x = 0. Here's how you can do it:

  1. Evaluate f(0)f(0):

    • Look at the graph of f(x)f(x) (the red curve) and find the value of f(0)f(0).
    • From the graph, at x=0x = 0, f(0)=1f(0) = 1.
  2. Evaluate g(0)g(0):

    • Look at the graph of g(x)g(x) (the blue line) and find the value of g(0)g(0).
    • From the graph, at x=0x = 0, g(0)=2g(0) = 2.
  3. Calculate (fg)(0)(f - g)(0): (fg)(0)=f(0)g(0)=12=1(f - g)(0) = f(0) - g(0) = 1 - 2 = -1

So, (fg)(0)=1(f - g)(0) = -1.

Would you like any further explanation or have any additional questions?


Here are some related questions to deepen your understanding:

  1. How would you interpret the graph of the function f(x)g(x)f(x) - g(x)?
  2. What is the domain of the difference of two functions?
  3. How do you determine the range of f(x)g(x)f(x) - g(x)?
  4. Can you express (f+g)(x)(f + g)(x) using the same steps we used here?
  5. How does the vertical translation of a function affect its graph?

Tip: Always carefully observe the signs when subtracting functions, as it can significantly affect the outcome.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Functions
Subtraction of Functions

Formulas

-

Theorems

-

Suitable Grade Level

Grades 10-12