Question

1. (0 points) let \\(f\\) and \\(g\\) be two functions defined below.

\\f(x) = \frac{1}{4x - 6} \quad \text{and} \quad g(x) = 5x - 1\\

calculate the following. combine and simplify.

(a) \\((f + g)(x) = \\)

Explanation:

Step1: Write the sum of functions

$$(f+g)(x) = f(x) + g(x) = \frac{1}{4x - 6} + (5x - 1)$$

Step2: Find a common denominator

$$(f+g)(x) = \frac{1 + (5x - 1)(4x - 6)}{4x - 6}$$

Step3: Expand the numerator

$$(5x - 1)(4x - 6) = 20x^2 - 30x - 4x + 6 = 20x^2 - 34x + 6$$

Step4: Simplify the final expression

$$(f+g)(x) = \frac{1 + 20x^2 - 34x + 6}{4x - 6} = \frac{20x^2 - 34x + 7}{4x - 6}$$

Answer:

$$(f+g)(x) = \frac{20x^2 - 34x + 7}{4x - 6}$$