Could you please check my answers and help me with one of them?
Find the inverse of the one to one function
1. f(x)-4x+7
-I got f^-1(x)=x-7/(-4)
2. f(x)= square root of x-8
-I got f^-1(x)=x^2-8
3. f(x)=4/(5x-1)
This one I don't understand how to find the inverse of the one to one function.
Why is the square of an addiction : (a+b)^2 = a^2+b^2 +2ab? Write an example describing the operation.
To find the inverse of a one-to-one function, you need to switch the roles of x and y, and then solve for y.
Let's go through the process for the third function, f(x) = 4/(5x-1):
Step 1: Replace f(x) with y: y = 4/(5x-1)
Step 2: Swap x and y: x = 4/(5y-1)
Step 3: Solve for y: Multiply both sides by (5y-1) to eliminate the denominator: x(5y-1) = 4
Step 4: Expand the equation: 5xy - x = 4
Step 5: Isolate y: Move the term with y to one side: 5xy = x + 4
Step 6: Divide by 5x: y = (x + 4) / (5x)
So, the inverse of the function f(x) = 4/(5x-1) is f^(-1)(x) = (x + 4) / (5x).
Now you can compare your result with the steps explained above to check if you obtained the correct answer.