Questions: If the point (6,10) is on the graph of y=f(x), which point must be on the graph of y=1/(2f(x))?

Transcript text: 7. If the point $(6,10)$ is on the graph of $y=f(x)$, which point must be on the graph of $y=\frac{1}{2 f(x)}$ ?

Solution

Solution Steps

Step 1: Understand the given information

We are given that the point $(6, 10)$ lies on the graph of $y = f(x)$. This means that when $x = 6$, $f(x) = 10$. Mathematically, this is written as: \[ f(6) = 10. \]

Step 2: Substitute into the new function

We are asked to find a point on the graph of $y = \frac{1}{2 f(x)}$. Using the value of $f(6) = 10$, substitute $x = 6$ into the new function: \[ y = \frac{1}{2 f(6)} = \frac{1}{2 \cdot 10} = \frac{1}{20}. \]

Step 3: Identify the corresponding point

The corresponding point on the graph of $y = \frac{1}{2 f(x)}$ is $(6, \frac{1}{20})$.