Evaluate the function $f(x) = 3x + 7$ for $x = 2$.
Answer (2)
Substitute x = 2 into the function f ( x ) = 3 x + 7 .
Calculate 3 ( 2 ) + 7 .
Simplify the expression to get 6 + 7 = 13 .
The final result is 13 .
Explanation
Understanding the problem We are given the function f ( x ) = 3 x + 7 and we want to evaluate it at x = 2 . This means we need to substitute x = 2 into the expression for f ( x ) and simplify.
Substitution Substitute x = 2 into the function: f ( 2 ) = 3 ( 2 ) + 7
Simplification Now, we simplify the expression: f ( 2 ) = 6 + 7 = 13
Final result Therefore, the value of the function f ( x ) = 3 x + 7 at x = 2 is 13.
Examples
Imagine you are calculating the cost of a taxi ride. The taxi company charges a fixed fee of $7 plus 3 p er mi l e . I f yo u t r a v e l 2 mi l es , t h e t o t a l cos tw o u l d b ec a l c u l a t e d u s in g t h e f u n c t i o n f(x) = 3x + 7 , w h ere x i s t h e n u mb ero f mi l es . I n t hi sc a se , f(2) = 3(2) + 7 = 13$, so the total cost of the ride is $13. This is a practical application of evaluating a linear function.
To find the value of the function f ( x ) = 3 x + 7 at x = 2 , substitute 2 into the function, which results in f ( 2 ) = 13 .
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