Question

100 POINTS!!!! PLEASE HELP

What is (f−g)(x)?

f(x)=x^4−4x^2+4

g(x)=x^3−2x^2+4x−8

Answer 1

`(f-g)(x) =x^4-x^3-2x^2-4x+12`

Explanation:

• 
  `f(x) =x^4-4x^2+4` (Given)

• 
  `g(x) =x^3-2x^2+4x-8` (Given)

• 
  `\implies (f-g)(x) =(x^4-4x^2+4)-(x^3-2x^2+4x-8)`

• 
  `\implies (f-g)(x) =x^4-4x^2+4-x^3+2x^2-4x+8`

• 
  `\implies (f-g)(x) =x^4-x^3-4x^2+2x^2-4x+4+8`

• 
  `\implies (f-g)(x) =x^4-x^3-2x^2-4x+12`

Answer 2

• (f - g)(x) = x⁴ - x³ - 2x² - 4x + 12

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Given

Functions f an g

• f(x) = x⁴ − 4x² + 4
• g(x) = x³ − 2x² + 4x − 8

Find the composite function (f - g)(x)

• (f - g)(x) =
• f(x) - g(x) = x⁴ - 4x² + 4 - (x³ −-2x² + 4x - 8) =
• x⁴ - 4x² + 4 - x³ + 2x² - 4x + 8 =
• x⁴ - x³ - 2x² - 4x + 12