Question

F(x) = x^2+1

what is the inverse algebraically

Answer 1

The inverse of the function F(x) = x^2+1 is F^-1(x) = sqrt(x - 1).

Step-by-step explanation:

The inverse of a function is found by swapping the variables and solving for the new variable. Given the function F(x) = x^2+1, we can find the inverse algebraically as follows:

Step 1: Replace F(x) with y to get the equation y = x^2+1.

Step 2: Swap x and y to get x = y^2+1.

Step 3: Solve the equation for y. Subtract 1 from both sides: x - 1 = y^2. Take the square root of both sides: sqrt(x - 1) = y.

Therefore, the inverse of the function is F-1(x) = sqrt(x - 1).