Question

Find the inverse function of f
F(x)=under root 2+6x then find
F inverse of (x)= ;x>equal to 0

Answer 1

To find the inverse of f(x) = √(2 + 6x), we will switch the x and y variables and solve for y.

Let y = √(2 + 6x)

Now, solving for x:

x = √(2 + 6y)

Squaring both sides to eliminate the square root:

x^2 = 2 + 6y

Rearranging the equation:

6y = x^2 - 2

Dividing both sides by 6:

y = (x^2 - 2) / 6

Therefore, the inverse function of f(x) = √(2 + 6x) is:

F^(-1)(x) = (x^2 - 2) / 6