Question

23 find the domain of the function f(x) = 7x + 6 a. (-∞,0) ∪ (0,∞) b. (-∞,∞) c. -6,∞) d. (0,∞)

Explanation:

Step1: Identify Function Type

The function \( f(x) = 7x + 6 \) is a linear function (in the form \( f(x)=mx + b \), where \( m = 7 \) and \( b = 6 \)).

Step2: Determine Domain of Linear Function

For linear functions (polynomial functions of degree 1), there are no restrictions on the input \( x \) (no division by zero, no square roots of negative numbers, etc.). So \( x \) can be any real number. The set of all real numbers is represented as \( (-\infty, \infty) \).

Step3: Match with Options

Option A excludes \( x = 0 \), which is unnecessary for a linear function. Option C restricts \( x \geq - 6 \), which is incorrect. Option D restricts \( x>0 \), which is also incorrect. Option B, \( (-\infty, \infty) \), represents all real numbers, which is the domain of \( f(x)=7x + 6 \).

Answer:

B. \( (-\infty, \infty) \)