Answer:
Steps in order will be
[tex]1. y=\sqrt{7x-21}\\2. y^2=7x-21 \\ 3. y^2=7(x-3)\\4. \frac{y^2}{7}=x-3\\ 5. x=\frac{y^2}{7}+3\\6. f^{-1}(x)=\frac{1}{7}x^2+3 \:where\: x\geq 0[/tex]
Step-by-step explanation:
Consider the function [tex]f(x)=\sqrt{7x-21}[/tex]
We need to find [tex]f^{-1}(x)[/tex]
For finding [tex]f^{-1}(x)[/tex] replace f(x) with y
Step 1: Replace f(x) with y
[tex]y=\sqrt{7x-21}[/tex]
Now, solve for x
Step 2: Taking square on left side
[tex]y^2=(\sqrt{7x-21})^2\\y^2=7x-21[/tex]
Step 3 : take 7 common
[tex]y^2=7(x-3)[/tex]
Step 4 : Divide both sides by 7
[tex]\frac{y^2}{7}=x-3[/tex]
Step 5: Add 3 on both sides
[tex]\frac{y^2}{7}+3=x-3+3\\x=\frac{y^2}{7}+3[/tex]
Step 6: Replace x with y and x with [tex]f^{-1}(x)[/tex]
[tex]f^{-1}(x)=\frac{1}{7}x^2+3[/tex] where x≥0
Steps in order will be
[tex]1. y=\sqrt{7x-21}\\2. y^2=7x-21 \\ 3. y^2=7(x-3)\\4. \frac{y^2}{7}=x-3\\ 5. x=\frac{y^2}{7}+3\\6. f^{-1}(x)=\frac{1}{7}x^2+3 \:where\: x\geq 0[/tex]
Assuming one or 2 steps are missing in the diagram given.
