Consider the following.
[tex]g(x)=5 x+14[/tex]
(a) Find [tex]g(2)[/tex].
[tex]g(2)=24[/tex]
(b) Find [tex]g(-11)[/tex]
[tex]g(-11)=[/tex]
Answer (1)
Substitute x = − 11 into the function g ( x ) = 5 x + 14 .
Calculate 5 × ( − 11 ) = − 55 .
Add 14 to -55: − 55 + 14 = − 41 .
The final answer is − 41 .
Explanation
Understanding the problem We are given the function g ( x ) = 5 x + 14 . We need to find the value of g ( − 11 ) .
Substituting the value To find g ( − 11 ) , we substitute x = − 11 into the expression for g ( x ) : g ( − 11 ) = 5 ( − 11 ) + 14
Simplifying the expression Now, we simplify the expression: g ( − 11 ) = − 55 + 14 g ( − 11 ) = − 41
Final Answer Therefore, g ( − 11 ) = − 41 .
Examples
Imagine you're tracking the temperature change throughout the day. If the temperature at a certain time is given by a function like g ( x ) = 5 x + 14 , where x is the number of hours since midnight, you can find the temperature at any hour by substituting the value of x . For example, to find the temperature at 11 PM (23 hours since midnight), you would calculate g ( 23 ) . This helps in predicting temperature changes and planning activities accordingly.
