Math Problem Statement

f (x)= 2x + 4 g (x)= x + 3 Find (f - g) (1)

Solution

To find (fg)(1)(f - g)(1), we need to first determine the expression for f(x)g(x)f(x) - g(x) and then evaluate it at x=1x = 1.

  1. Find f(x)g(x)f(x) - g(x):

    f(x)=2x+4f(x) = 2x + 4 g(x)=x+3g(x) = x + 3 Subtracting g(x)g(x) from f(x)f(x):

    (fg)(x)=f(x)g(x)=(2x+4)(x+3)(f - g)(x) = f(x) - g(x) = (2x + 4) - (x + 3)

    Simplify the expression:

    (fg)(x)=2x+4x3=x+1(f - g)(x) = 2x + 4 - x - 3 = x + 1

  2. Evaluate (fg)(1)(f - g)(1):

    Substitute x=1x = 1 into the simplified expression:

    (fg)(1)=1+1=2(f - g)(1) = 1 + 1 = 2

So, (fg)(1)=2(f - g)(1) = 2.

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:

  1. What is (f+g)(1)(f + g)(1) using the same functions f(x)f(x) and g(x)g(x)?
  2. How would you find (fg)(x)(f \cdot g)(x) for the given functions?
  3. What is the derivative of (fg)(x)(f - g)(x)?
  4. How would you determine (fg)(x)(f \circ g)(x) for these functions?
  5. If h(x)=f(x)g(x)h(x) = f(x) - g(x), what is the value of h(2)h(2)?

Tip: When combining functions, always simplify the expressions before evaluating them at a specific value.

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Math Problem Analysis

Mathematical Concepts

Functions
Subtraction of Functions
Evaluation of Functions

Formulas

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Theorems

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Suitable Grade Level

High School