Question

If f(x)=2x², find f(6).

Answer 1

To find
`\( f(6) \)`, substitute ( x = 6 ) into the function
`\( f(x) = 2x^2 \)`:
`\[ f(6) = 2 * (6^2) = 2 * 36 = 72. \]`

Explanation:

To determine ( f(6) ) for the function
`\( f(x) = 2x^2 \)`, substitute ( x = 6 ) into the expression. The process involves squaring the value of ( x ) and then multiplying it by the coefficient 2. In this specific case, ( f(6) ) is calculated as follows:
`\( 2 * (6^2) = 2 * 36 = 72 \)`. Therefore, the final answer is
`\( f(6) = 72 \)`.

Understanding function notation is pivotal in mathematics. The notation
`\( f(x) \)` represents a mathematical function, where ( x ) is the input variable. When we evaluate ( f ) at a specific value of ( x ), denoted as ( f(a) ), it yields the corresponding output of the function at that particular input. In this scenario, ( f(6) ) signifies finding the output of the function when ( x ) equals 6.

This concept is fundamental in calculus, algebra, and various mathematical applications, forming the basis for analyzing relationships between variables. The substitution process demonstrated here is a fundamental operation in algebraic manipulation and is frequently employed when working with mathematical functions.