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))?

Solution Steps

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: $$f(6) = 10.$$

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: $$y = \frac{1}{2 f(6)} = \frac{1}{2 \cdot 10} = \frac{1}{20}.$$

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

Final Answer