Question

Drag each tile to the correct box. Not all tiles will be used. Consider function f. ​

Answer 1

Answer:

Steps in order will be

$1. y=\sqrt{7x-21}\\2. y^2=7x-21 \\ 3. y^2=7(x-3)\\4. \frac{y^2}{7}=x-3\\ 5. x=\frac{y^2}{7}+3\\6. f^{-1}(x)=\frac{1}{7}x^2+3 \:where\: x\geq 0$

Step-by-step explanation:

Consider the function $f(x)=\sqrt{7x-21}$

We need to find $f^{-1}(x)$

For finding $f^{-1}(x)$  replace f(x) with y

Step 1: Replace f(x) with y

$y=\sqrt{7x-21}$

Now, solve for x

Step 2: Taking square on left side

$y^2=(\sqrt{7x-21})^2\\y^2=7x-21$

Step 3 : take 7 common

$y^2=7(x-3)$

Step 4 : Divide both sides by 7

$\frac{y^2}{7}=x-3$

Step 5: Add 3 on both sides

$\frac{y^2}{7}+3=x-3+3\\x=\frac{y^2}{7}+3$

Step 6: Replace x with y and x with $f^{-1}(x)$

$f^{-1}(x)=\frac{1}{7}x^2+3$ where x≥0

Steps in order will be

$1. y=\sqrt{7x-21}\\2. y^2=7x-21 \\ 3. y^2=7(x-3)\\4. \frac{y^2}{7}=x-3\\ 5. x=\frac{y^2}{7}+3\\6. f^{-1}(x)=\frac{1}{7}x^2+3 \:where\: x\geq 0$

Assuming one or 2 steps are missing in the diagram given.

Answer 2

Answer:

1. y=√7x-21

2. x=√7x-21

3. x^2 = 7y -21

4. x^2+21= 7y

5. 1/7x^2+3=y

6. 1/7x^2 + 3 = f^-1(x), where x≥0

Step-by-step explanation:

just got it correct on the test