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frutty [35]
3 years ago
8

Let f(x)=4x-1 and g(x)=2x^2+3. Perform each function operations and then find the domain.

Mathematics
1 answer:
Triss [41]3 years ago
6 0
F(x) = 4x - 1
g(x) = 2x² + 3

1. (f + g)(x) = (4x - 1) + (2x² + 3)
    (f + g)(x) = 2x² + 4x + (-1 + 3)
    (f + g)(x) = 2x² + 4x + 2
    Domain: {x| -∞ < x < ∞}, (-∞, ∞)

2. (f - g)(x) = (4x + 1) - (2x² + 3)
    (f - g)(x) = 4x + 1 - 2x² - 3
    (f - g)(x) = -2x² + 4x + 1 - 3
    (f - g)(x) = -2x² + 4x - 2
    Domain: {x|-∞ < x < ∞}, (-∞, ∞)
3. (g - f)(x) = (2x² + 3) - (4x - 1)
    (g - f)(x) = 2x² + 3 - 4x + 1
    (g - f)(x) = 2x² - 4x + 3 + 1
    (g - f)(x) = 2x² - 4x + 4
    Domain: {x| -∞ < x < ∞}, (-∞, ∞)

4. (f · g)(x) = (4x + 1)(2x² + 3)
    (f · g)(x) = 4x(2x² + 3) + 1(2x² + 3)
    (f · g)(x) = 4x(2x²) + 4x(3) + 1(2x²) + 1(3)
    (f · g)(x) = 8x³ + 12x + 2x² + 3
    (f · g)(x) = 8x³ + 2x² + 12x + 3
    Domain: {x| -∞ < x < ∞}, (-∞, ∞)

5. (\frac{f}{g})(x) = \frac{4x - 1}{2x^{2} + 3}
    Domain: 2x² + 3 ≠ 0
                         - 3  - 3
                        2x² ≠ 0
                         2      2
                          x² ≠ 0
                           x ≠ 0
                  (-∞, 0) ∨ (0, ∞)

6. (\frac{g}{f})(x) = \frac{2x^{2} + 3}{4x - 1}
    Domain: 4x - 1 ≠ 0
                      + 1 + 1
                        4x ≠ 0
                         4     4
                         x ≠ 0
                (-∞, 0) ∨ (0, ∞)
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