If $f(x)=14 x-16$, calculate $f(-15)$
Answer (1)
Substitute x = − 15 into the function f ( x ) = 14 x − 16 .
Calculate 14 × ( − 15 ) = − 210 .
Subtract 16 from -210: − 210 − 16 = − 226 .
The final answer is − 226 .
Explanation
Understanding the problem We are given the function f ( x ) = 14 x − 16 and asked to find the value of f ( − 15 ) . This means we need to substitute − 15 for x in the expression for f ( x ) .
Substitution Now, let's substitute x = − 15 into the function: f ( − 15 ) = 14 × ( − 15 ) − 16
Multiplication Next, we perform the multiplication: 14 × ( − 15 ) = − 210
Substituting the result Now, substitute this result back into the expression: f ( − 15 ) = − 210 − 16
Subtraction Finally, we perform the subtraction: f ( − 15 ) = − 226
Final Answer Therefore, f ( − 15 ) = − 226 .
Examples
In real life, functions like this can model various scenarios. For example, imagine a store offers a discount program where customers get a $16 discount after spending $14 for each item. If a customer buys 15 items, the total cost can be calculated using this function. Substituting the number of items into the function gives the final cost after the discount. This helps in understanding the relationship between the number of items purchased and the final cost.
