Question

If f(x)=√3x+2

​, what is the equation for f^−1(x)?

A) f^−1(x)=√x−2
​
B) f^−1(x)=x²−2 / 3
C) f^−1(x)=x²−2 / 3x​
D) f^−1(x)=x²−4 / 3

Answer 1

The equation for the inverse function, f^−1(x), is f^−1(x) = (x-2)/√3.

Step-by-step explanation:

The equation for the inverse function, f^−1(x), can be found by interchanging the x and y variables and solving for y. In this case, the given function is f(x) = √3x+2. To find f^−1(x), we interchange x and y to get x = √3y+2. Next, we solve for y:

x = √3y+2

x-2 = √3y

(x-2)/√3 = y

So the equation for f^−1(x) is f^−1(x) = (x-2)/√3, which corresponds to option A.