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Consider the function [tex]f(x)=\sqrt{7x-21}[/tex].

Place the steps for finding [tex]f^{-1}(x)[/tex] in the correct order.

[tex]
\begin{array}{c}
1. x=\sqrt{7y-21} \\
2. x^2=7y-21 \\
3. x^2+21=7y \\
4. \frac{1}{7}\left(x^2-21\right)=f^{-1}(x), \text{ where } x \geq 0 \\
\hline
\end{array}
[/tex]


Sagot :

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]
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