Question

2. Write the inverse function equation for the given function equation. f(x) = - 7 + √3x

​a) Let y = f(x).
b) Swap x and y in the equation: x = -7 + √3y.
c) Solve for y to find the inverse function

Answer 1

To find the inverse of the function f(x) = -7 + \sqrt{3x}, let y = -7 + \sqrt{3x}, then swap x and y to get x = -7 + \sqrt{3y}, and solve for y to obtain the inverse function f^{-1}(x) = \frac{(x + 7)^2}{3}. The correct answer is option B .

Step-by-step explanation:

Finding the inverse function equation for f(x) = -7 + \sqrt{3x} involves a few crucial steps to isolate y and swap the inputs and outputs:

1. Firstly, we express the function as y = f(x). So, we start by letting y = -7 + \sqrt{3x}.

2. Next, we swap x and y to get x = -7 + \sqrt{3y}. This is critical for determining the inverse.

3. We then solve for y. To do this, we first isolate the square root term: \sqrt{3y} = x + 7. Squaring both sides to eliminate the square root gives us 3y = (x + 7)^2.

4. Finally, divide by 3 to solve for y, resulting in the inverse function: y = \frac{(x + 7)^2}{3}.

To represent it as an inverse function, we use the notation f^{-1}(x). Therefore, the inverse function equation is f^{-1}(x) = \frac{(x + 7)^2}{3}.