To determine the steps for finding the inverse of the function [tex]\( f(x) = \sqrt{7x - 21} \)[/tex], we can arrange the following steps in the correct order:
1. Start with [tex]\( x = \sqrt{7y - 21} \)[/tex]
2. Square both sides to remove the square root:
[tex]\[ x^2 = 7y - 21 \][/tex]
3. Add 21 to both sides to isolate the [tex]\( y \)[/tex]-term:
[tex]\[ x^2 + 21 = 7y \][/tex]
4. Solve for [tex]\( y \)[/tex] by dividing both sides by 7:
[tex]\[ y = \frac{1}{7} (x^2 + 21), \text{ where } x \geq 0 \][/tex]
Arranging the given steps, the correct order is:
1. [tex]\( x = \sqrt{7y - 21} \)[/tex]
2. [tex]\( x^2 = 7y - 21 \)[/tex]
3. [tex]\( x^2 + 21 = 7y \)[/tex]
4. [tex]\( \frac{1}{7}(x^2 + 21) = f^{-1}(x), \text{ where } x \geq 0 \)[/tex]
So, the steps in order should be:
1. [tex]\( x = \sqrt{7 y - 21} \)[/tex]
2. [tex]\( x^2 = 7 y - 21 \)[/tex]
3. [tex]\( x^2 + 21 = 7 y \)[/tex]
4. [tex]\( \frac{1}{7}(x^2 + 21) = f^{-1}(x), \text { where } x \geq 0 \)[/tex]
