Question

PLEASE HELP 100 POINTS

The function f(x) represents the number of texts sent this week, and g(x) represents the number of texts sent last week. Given f(x) = 8x + 14 and g(x) = 5x − 2, find (f − g)(x) to find how many more texts were sent this week than last week.

A:(f − g)(x) = 3x + 12
B: (f − g)(x) = 3x + 16
C: (f − g)(x) = 13x + 12
D: (f − g)(x) = 13x + 16

Answer 1

The function that represents how many more texts that were sent this week than last week is: B. (f − g)(x) = 3x + 16.

How to Evaluate Functions?

To find the value of a given functional expression, we have to apply the basic knowledge of how to solve algebraic expressions.

For example, if we are given that (f - g)(x), it means we are to subtract the function g(x) from f(x). That is (f - g)(x) = f(x) - g(x).

Given the following functions:

Number of texts sent this week is represented as the function, f(x) = 8x + 14

Number of texts sent last week is represented as the function, g(x) = 5x - 2.

Number of texts that were sent this week than last week = (f - g)(x)

(f - g)(x) = (8x + 14) - (5x - 2)

(f - g)(x) = 8x + 14 - 5x + 2

(f - g)(x) = 3x + 16

Therefore, the answer is: (f − g)(x) = 3x + 16.

Answer 2

Explanation:

To find (f - g)(x), we need to subtract the function g(x) from the function f(x).

(f - g)(x) = f(x) - g(x)

Substituting the given functions for f(x) and g(x), we get:

(f - g)(x) = (8x + 14) - (5x - 2)

Simplifying this expression, we get:

(f - g)(x) = 8x + 14 - 5x + 2

(f - g)(x) = 3x + 16

Therefore, the answer is B: (f − g)(x) = 3x + 16.