Question

Find the inverse function for f(x)= sqrt2x-6

Answer 1

To find the inverse function of f(x) = sqrt(2x) - 6, we need to switch the variables x and y and solve for y.

So, let's begin by switching the variables:

x = sqrt(2y) - 6

Now, let's isolate the term with the square root:

x + 6 = sqrt(2y)

To remove the square root, we square both sides of the equation:

(x + 6)^2 = (sqrt(2y))^2

Simplifying both sides:

(x + 6)^2 = 2y

Next, we divide both sides by 2:

((x + 6)^2)/2 = y

Thus, the inverse function is given by:

f^(-1)(x) = ((x + 6)^2)/2