For the function f(p) an input of 3 yields an output value of 6. What value of p would you use to have f(5p) = 6?
To find the value of p that would make f(5p) equal to 6, we can start by substituting 5p into the function f(p).
Given that f(p) = 6 when the input p = 3, we have:
f(3) = 6
Now, let's substitute 5p into the function:
f(5p) = 6
To find the value of p, we need to isolate p on one side of the equation.
First, let's divide both sides of the equation by 5:
f(5p)/5 = 6/5
Simplifying further, we have:
f(p) = 6/5
Since we are looking for the value of p that would make f(5p) equal to 6, we can equate the function f(p) with 6/5:
f(p) = 6/5
Now, recall that we are also given that f(p) = 6 when p = 3. So we can substitute 3 into the equation:
f(3) = 6/5
Since we know that f(3) = 6, we can write:
6 = 6/5
Now, to solve for the value of p, we can cross-multiply and solve for p:
6 * 5 = 6 * p
30 = 6p
Finally, dividing both sides of the equation by 6, we find:
p = 30/6
Therefore, the value of p that would make f(5p) equal to 6 is p = 5.