f(x)= 1/x, x greater than 7
3x, x less than or equal to 7
Find f(7t)
To find f(7t), we need to determine the value of f(x) when x is equal to 7t.
Given the function f(x) defined as:
f(x) = 1/x, for x greater than 7
f(x) = 3x, for x less than or equal to 7
We can substitute 7t for x in the respective parts of the function according to the given conditions.
When x > 7, f(x) = 1/x. So, when 7t > 7, we apply this part of the function.
When 7t > 7, dividing both sides by 7 gives us t > 1.
Therefore, when t > 1, f(7t) = 1/(7t).
When x ≤ 7, f(x) = 3x. So, when 7t ≤ 7, we apply this part of the function.
When 7t ≤ 7, dividing both sides by 7 gives us t ≤ 1.
Therefore, when t ≤ 1, f(7t) = 3(7t) = 21t.
In summary, we have:
- If t > 1, f(7t) = 1/(7t).
- If t ≤ 1, f(7t) = 21t.