Consider the following.
[tex]g(x)=5 x+14[/tex]
(a) Find [tex]g(2)[/tex].
[tex]g(2)=[/tex]
Answer (1)
Substitute x = 2 into the function g ( x ) = 5 x + 14 .
Calculate 5 × 2 = 10 .
Add 10 and 14 to get 10 + 14 = 24 .
The final answer is 24 .
Explanation
Understanding the problem We are given the function g ( x ) = 5 x + 14 and asked to find the value of g ( 2 ) . This means we need to substitute x = 2 into the expression for g ( x ) .
Substituting x=2 To find g ( 2 ) , we replace x with 2 in the expression for g ( x ) : g ( 2 ) = 5 ( 2 ) + 14
Calculating g(2) Now, we perform the calculation: g ( 2 ) = 10 + 14 g ( 2 ) = 24
Final Answer Therefore, the value of g ( 2 ) is 24.
Examples
In real life, this type of function can model various scenarios. For example, imagine a taxi service charges a fixed fee of $14 plus $5 per mile. If you travel 2 miles, the total cost would be calculated as g(2) = 5(2) + 14 = $24. This demonstrates how a linear function can represent costs, distances, or any relationship with a constant rate of change.
