Inverses of the Functions.

What does it mean to find the inverse of a function?

• the x's and y's are switched
• the x's and y's are divided by 2
• the x's and y's are made negative
• the x's and y's are the same

Tags

TEKS.MATH.P.2E

Find the inverse of  $f\left(x\right)=3x+2$  

•  $f^{-1}\left(x\right)=\frac{x-2}{3}$  

•  $f^{-1}\left(x\right)=\frac{x-3}{2}$  

•  $f^{-1}\left(x\right)=\frac{3x}{2}$  

•  $f^{-1}\left(x\right)=\frac{2+x}{3}$  

Tags

TEKS.MATH.P.2E

Find the inverse of  $f\left(x\right)=-5x-7$  

•  $f^{-1}\left(x\right)=\frac{5x+7}{-7}$  

•  $f^{-1}\left(x\right)=\frac{x+5}{7}$  

•  $f^{-1}\left(x\right)=\frac{x+7}{-5}$  

•  $f^{-1}\left(x\right)=\frac{7}{-5+x}$  

Tags

CCSS.HSF-BF.B.4A

Find the inverse of  $f\left(x\right)=12x-3$  

•  $f^{-1}\left(x\right)=\frac{x+3}{12}$  

•  $f^{-1}\left(x\right)=\frac{x-3}{12}$  

•  $f^{-1}\left(x\right)=\frac{x+12}{3}$  

•  $f^{-1}\left(x\right)=\frac{x-12}{3}$  

Tags

CCSS.HSF-BF.B.4A

Find the inverse for this relation: { (1, -3), (-2, 3), (5, 1), (6, 4) }

• { (1, 3), (2, 3), (5, 1), (6, 4) }

• { (-1, -3), (-2, -3), (-5, -1), (-6, -4) }

• { (3, -1), (-3, 2), (-5, 1), (4, -6) }

• { (-3, 1), (3, -2), (1, 5), (4, 6) }

Tags

CCSS.HSF-BF.B.4C

Are f(x) =x+6 and g(x) =x-6 inverses?

• Yes

• No

Tags

CCSS.HSF-BF.B.4B

Graph the inverse

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Tags

CCSS.HSF-BF.B.4C

To graph the inverse of a function...

• Rotate it around the origin

• Reflect it across the x-axis

• Reflect it across the y-axis

• Switch the x and y coordinates and plot the new points

Tags

CCSS.HSF-BF.B.4C

When two functions are inverses of each other, their graphs are reflective over...

• y=x

• x-axis

• y-axis

Tags

CCSS.HSF-BF.B.4C

To prove two functions are inverses of each other, both f(g(x)) and g(f(x) should equal...

• 1

• x

• 0

• y

Tags

CCSS.HSF-BF.B.4B