Question

For the function q(x) = 10√x-2, what is the inverse function?

Answer 1

To find the inverse of the function q(x) = 10√x - 2, swap x and y, perform algebraic operations to isolate y, and obtain q⁻¹(x) = ((x + 2)/10)² as the inverse function.

Step-by-step explanation:

To find the inverse function of q(x) = 10√x - 2, we need to swap x and y and then solve for the new y. Let's start by rewriting the function as y = 10√x - 2 and then swap to get x = 10√y - 2.

Now, we will isolate the square root term by adding 2 to both sides, yielding x + 2 = 10√y.

Next, divide both sides by 10 to get (x + 2)/10 = √y.

Finally, square both sides to eliminate the square root and solve for y, resulting in y = ((x + 2)/10)^2.

So, the inverse function of q(x) is q-1(x) = ((x + 2)/10)^2.