Inverse relations and functions
finding the inverse function
step 1: determine whether the function has an inverse, by checking to see if it is one-to-one using the horizontal line test.
step 2: in the equation for f(x), replace f(x) with y and then interchange x and y.
step 3: solve for y and then replace the y with f^-1(x) in the new equation.
step 4: State any restrictions on the domain of f^-1 then show that the domain of f is equal to the range of f^-1 anD the range of f is =the domain f-1.
step 1: determine whether the function has an inverse, by checking to see if it is one-to-one using the horizontal line test.
step 2: in the equation for f(x), replace f(x) with y and then interchange x and y.
step 3: solve for y and then replace the y with f^-1(x) in the new equation.
step 4: State any restrictions on the domain of f^-1 then show that the domain of f is equal to the range of f^-1 anD the range of f is =the domain f-1.
1. Mult. each side by denom. so it cancles.
2. Add/Sub_x on each side.
3.Do it again to get all variables on one side
4. gcf of (x) or (y)
5. Divide each side
To Find Inverse
Step1: use horizontal line test to see if it has an inverse
Step2: Switch x and y in equation
Step3: solve for y
f^-1 (x)=inverse
Step4: state restrictions
2. Add/Sub_x on each side.
3.Do it again to get all variables on one side
4. gcf of (x) or (y)
5. Divide each side
To Find Inverse
Step1: use horizontal line test to see if it has an inverse
Step2: Switch x and y in equation
Step3: solve for y
f^-1 (x)=inverse
Step4: state restrictions