Given the following functions, find each: $$ f(x)=x^{2}+3 x-28 $$ $$ g(x)=x+7 $$ $$ (f+g)(x)=\square $$ $$ (f-g)(x)=\square $$ $$ (f \cdot g)(x)=\square $$

Question

UpStudy AI · Accepted Answer

We are given two functions:
  f(x) = x² + 3x – 28
  g(x) = x + 7

Step 1: Find (f + g)(x)
  Add the two functions:
   (f + g)(x) = f(x) + g(x)
    = (x² + 3x – 28) + (x + 7)
    = x² + (3x + x) + (–28 + 7)
    = x² + 4x – 21

Step 2: Find (f – g)(x)
  Subtract g(x) from f(x):
   (f – g)(x) = f(x) – g(x)
    = (x² + 3x – 28) – (x + 7)
    = x² + (3x – x) + (–28 – 7)
    = x² + 2x – 35

Step 3: Find (f ⋅ g)(x)
  Multiply the two functions:
   (f ⋅ g)(x) = f(x) · g(x)
    = (x² + 3x – 28)(x + 7)

Expand the product:
  Multiply each term in the first factor by each term in the second factor:
   x² · x = x³
   x² · 7 = 7x²
   3x · x = 3x²
   3x · 7 = 21x
   (–28) · x = –28x
   (–28) · 7 = –196

Combine like terms:
  x³ + (7x² + 3x²) + (21x – 28x) – 196
  = x³ + 10x² – 7x – 196

Final Answers:
  (f + g)(x) = x² + 4x – 21
  (f – g)(x) = x² + 2x – 35
  (f ⋅ g)(x) = x³ + 10x² – 7x – 196
$$ (f + g)(x) = x^2 + 4x - 21 \ (f - g)(x) = x^2 + 2x - 35 \ (f \cdot g)(x) = x^3 + 10x^2 - 7x - 196 $$

Given the following functions, find each: \( f(x)=x^{2}+3 x-28 \) \( g(x)=x+7 \) \( (f+g)(x)=\square \) \( (f-g)(x)=\square \) \( (f \cdot g)(x)=\square \)

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Algebra Questions