Inverse of f(x)=(1/4x)+2
y = (1/4)x + 2
step 1 of finding the inverse: interchange the x and y variables
x = (1/4)y + 2
step 2 : solve this new equation for y
4x = y + 8
y = 4x - 8
step 3: state conclusion
f^-1 (x) = 4x - 8
To find the inverse of a function, we can follow these steps:
Step 1: Replace f(x) with y. The given function is f(x) = (1/4x) + 2, so we have y = (1/4x) + 2.
Step 2: Swap x and y. Replace y with x and x with y. We now have x = (1/4y) + 2.
Step 3: Solve the equation for y. To find the inverse function, we need to rewrite the equation in terms of y. Let's isolate y by subtracting 2 from both sides:
x - 2 = 1/4y
Step 4: Multiply both sides by 4 to eliminate the fraction:
4(x - 2) = y
Simplifying the equation, we get:
4x - 8 = y
So, the inverse function of f(x) = (1/4x) + 2 is given by f^(-1)(x) = 4x - 8.
Regarding the answer to your specific question, the inverse of the function f(x)=(1/4x)+2 is f^(-1)(x) = 4x - 8.