f (x) = 560 + 40x. (a) Find a formula for the inverse function f �1
if y = f(x) then x = f-1(y)
so.
y = 560+40x
7-560 = 40x
(y-560)/40 = x
so,
f-1(x) = (x-560)/40
Why did the function go to a therapist? Because it wanted to find its inverse!
To find the inverse function f^(-1), let's start by replacing f(x) with y:
y = 560 + 40x
Next, let's swap x and y:
x = 560 + 40y
Now, let's solve for y:
x - 560 = 40y
Divide both sides by 40:
(you - 14) = y
So, the formula for the inverse function f^(-1) is:
f^(-1)(y) = (x - 560) / 40
Remember, this is a clown-approved answer!
To find the inverse function of f(x), we need to switch the roles of x and f(x) and solve for x. Let's call the inverse function f^(-1)(x).
We start by writing the equation:
f(x) = 560 + 40x
Switching the roles of x and f(x), we have:
x = 560 + 40f^(-1)(x)
Now, let's solve this equation for f^(-1)(x):
1. Subtract 560 from both sides of the equation:
x - 560 = 40f^(-1)(x)
2. Divide both sides of the equation by 40:
(x - 560)/40 = f^(-1)(x)
Simplifying further:
f^(-1)(x) = (x - 560)/40
Therefore, the formula for the inverse function f^(-1)(x) is (x - 560)/40.
To find the formula for the inverse function f^(-1), we need to interchange the "x" and "f(x)" variables and solve for "x".
Step 1: Start with the function f(x) = 560 + 40x.
Step 2: Replace f(x) with "x" and x with "f(x)" to obtain x = 560 + 40(f^(-1)).
Step 3: Solve the equation for f^(-1) to isolate the variable. Subtract 560 from both sides of the equation: x - 560 = 40(f^(-1)).
Step 4: Divide both sides of the equation by 40 to solve for f^(-1): (x - 560)/40 = f^(-1).
Therefore, the formula for the inverse function f^(-1) is given by f^(-1)(x) = (x - 560)/40.