Question

"let f [x] =7x²-5x+3 and g [x] = 2x²+ 4x-6

part a find f [x]+ g [ x]
part b find f [x]-g [x]
part c find g [x] - f [x]"

Answer 1

Algebraic addition and subtraction are used to find the sum and differences of the functions f[x] and g[x], resulting in three new polynomial expressions for each of the parts, respectively.

Step-by-step explanation:

To find f[x] + g[x], f[x] - g[x], and g[x] - f[x], we simply need to perform algebraic addition and subtraction of the two given functions.

1. Part A: To find f[x] + g[x], add the corresponding coefficients of the like terms from both polynomials.
   f[x] + g[x] = (7x² + 2x²) - (5x + 4x) + (3 - 6)
   f[x] + g[x] = 9x² - 9x - 3

2. Part B: For f[x] - g[x], subtract the coefficients of g[x] from f[x].
   f[x] - g[x] = (7x² - 2x²) - (5x - 4x) + (3 - (-6))
   f[x] - g[x] = 5x² - x + 9

3. Part C: Finally, for g[x] - f[x], subtract the coefficients of f[x] from g[x].
   g[x] - f[x] = (2x² - 7x²) + (4x + 5x) - (6 - 3)
   g[x] - f[x] = -5x² + 9x - 3