Question Find a function $f(x)$ that represents the product of two numbers $x$ and $y$ whose sum is 24.

Studdy Solution

STEP 1

Assumptions1. We have two numbers $x$ and $y$ . . The sum of these two numbers is24, i.e., $x + y =24$ .
3. We need to express the product of these two numbers, $x \cdot y$ , as a function of one variable $x$ .

STEP 2

We can express $y$ as a function of $x$ using the equation $x + y =24$ . $y =24 - x$

STEP 3

Now, we can express the product of $x$ and $y$ as a function of $x$ by substituting $y$ with $24 - x$ .
$f(x) = x \cdot y = x \cdot (24 - x)$

STEP 4

We can simplify the function $f(x)$ .
$f(x) =24x - x^2$ So, the product of two numbers $x$ and $y$ whose sum is24 can be expressed as the function $f(x) =24x - x^2$ .

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