Math Problem Statement

F(×)=4×+2 g(×)=3×-1. Find (f-g)(4).

Solution

To find (fg)(4)(f - g)(4), we need to calculate f(4)f(4) and g(4)g(4) separately and then subtract g(4)g(4) from f(4)f(4).

  1. Calculate f(4)f(4): f(x)=4x+2f(x) = 4x + 2 Substituting x=4x = 4: f(4)=4(4)+2=16+2=18f(4) = 4(4) + 2 = 16 + 2 = 18

  2. Calculate g(4)g(4): g(x)=3x1g(x) = 3x - 1 Substituting x=4x = 4: g(4)=3(4)1=121=11g(4) = 3(4) - 1 = 12 - 1 = 11

  3. Calculate (fg)(4)(f - g)(4): (fg)(4)=f(4)g(4)=1811=7(f - g)(4) = f(4) - g(4) = 18 - 11 = 7

So, (fg)(4)=7(f - g)(4) = 7.

Would you like further details or have any questions?

Related Questions:

  1. How do you find the sum of f(x)f(x) and g(x)g(x) at a given xx value?
  2. What is the result of (fg)(4)(f \cdot g)(4)?
  3. How would you solve (f/g)(4)(f/g)(4)?
  4. How do you find the derivative of f(x)f(x) and g(x)g(x)?
  5. What is the solution to f(x)=g(x)f(x) = g(x)?

Tip: Always check your function calculations step-by-step to ensure accuracy, especially when combining functions!

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Function Operations

Formulas

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

Theorems

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Suitable Grade Level

Grades 8-10