Given f(x) = the quantity of x plus 7, divided by 5, solve for f−1(3).
Functions are very important concepts in mathematics that form the backbone of topics like calculus. The fundamental operations can be performed on two or more functions to give a new function as a result.
Answer: For f(x) = the quantity of x plus 7, divided by 5, f-1(3) = 8.
We will use inverse of function formula to answer this question. Let's understand the solution in detail.
From the questions, it is given that f(x) = (x + 7) / 5.
To find the inverse of the function, we follow the steps below:
Step 1: First we write f(x) = y.
⇒ Hence, f(x) = y = (x + 7) / 5
Step 2: Now we find x in terms of y.
⇒ Hence, x = 5y - 7
Step 3: Finally, we substitute x with f-1(x) and y with x to get the final solution.
⇒ Hence, f-1(x) = 5x - 7.
Therefore, from the above equation, f-1(3) = 8.