Monday 2.22 Alg 2 Inverse Functions

Monday 2.22 Alg 2 Inverse Functions Updated

Open Ended

2.22    Warm up  

 $f\left(x\right)=\ x\ +\ 3\ \ \ \ \ \ \ g\left(x\right)=x\ -\ 3$   $Find\ f\left(g\left(x\right)\right),\ \ then\ find\ g\left(f\left(x\right)\right).\ \ \$  

What do you notice about the answers? 

Put your results and your observation in the chat!

Multiple Choice

The inverse has been reflected over which line?

• y = x
• y =1
• y = 0
• y = x + 1

Multiple Choice

What is the inverse of the given coordinates: (1, 2) (3, 8) (-3, 6)

• (1, 2) (3, 8) (-3, 6)

• (1, 2) (8, 3) (-3, 6)

• (-1, -2) (-3, -8) (3, -6)

• (2, 1) (8, 3) (6, -3)

Multiple Choice

 $Are\ f\left(x\right)=2x-5\ and\ g\left(x\right)=\frac{1}{2}x\ +\ \frac{5}{2}\ inverse\ functions?\ \$ Why or why not? Be prepared to discuss.

• Yes

• No

You can also verify by graphing

https://www.desmos.com/calculator/6aoz88p3zr

Multiple Select

Select the two functions which are inverses of each other:

• $x+10$

• $x-10$

• $\frac{x}{10}$

• $\frac{10}{x}$

Multiple Choice

Are these functions inverses?

• Yes
• No

Multiple Select

Select the two functions which are inverses of each other:

• $x-4$

• $4x$

• $\frac{x}{4}$

• $\frac{4}{x}$

Multiple Choice

• Inverse Functions
• Not Inverse Functions

Multiple Choice

• Inverse Functions
• Not Inverse Functions

Multiple Choice

Was the inverse function found correctly?

• no
• yes

Multiple Choice

are these inverse functions?

• no
• yes
• no way to tell

Multiple Choice

If the equation of f(x) goes through (1, 4) and (4, 6), what points does f^-1(x) go through?

• (1, 4) and (4, 6)

• (-4, -1) and (-6, -4)

• (-1, -4) and (-4, -6)

• (4, 1) and (6, 4)

Multiple Choice

The inverse has been reflected over which line?

• y = x

• y =1

• y = 0

• y = x + 1

Multiple Choice

What is the first step in finding the equation of the inverse of a function?

• get x by itself

• switch x and y

• solve for y

• write the function in inverse function notation

Multiple Choice

What's the name of the inverse of g(x)?

• f(x)

• f^-1(x)

• y

• g^-1(x)

Multiple Choice

What operation allows us to verify if functions are inverses?

• Multiplying

• Dividing

• Adding

• Composing

Multiple Choice

What does an inverse function do?

• Nothing

• Makes it bigger

• Does the opposite of the original function

Fill in the Blanks

 $What\ is\ the\ first\ step\ if\ finding\ the\ inverse?$  

 $y=4x-5\$  

Multiple Choice

 $x=4y-5$   $What\ is\ the\ next\ step?$  

• Replace f(x) with y

• Solve for y

• Solve for x

• Replace x with y and y with x

Multiple Choice

Find the inverse of
f(x) = 1/4x - 7

• f^-1(x) = 4x + 7
• f^-1(x) = -4x + 28
• f^-1(x) = -4x - 7
• f^-1(x) = 4x + 28

Multiple Choice

Find the inverse of f(x) = -4x - 12

• f^-1(x) = 4x - 3
• f^-1(x) = -1/4x - 3
• f^-1(x) = 1/4x + 3
• f^-1(x) = -4x - 3