6.3 Quiz: Inverses of Exponentials and Logarithms

When you want to find the inverse of a function, you first

• Solve for y

• Change to exponential form

• Switch x and y

• Change to logarithmic form

Tags

CCSS.HSF-BF.B.4A

Find the inverse of: $y=\ln\left(x-4\right)$  

•  $y=e^x+4$  

•  $y=e^{x+4}$  

•  $y=e^x-4$  

•  $y=e^{x-4}$  

Tags

CCSS.HSF-BF.B.4A

Find the inverse of: $y=\log_{ }\left(x-2\right)+1$  

•  $y=\log\left(x-2\right)+1$  

•  $y=10^x-1$  

•  $y=10^{x-1}+2$  

•  $y=10^{x-2}-1$  

Tags

CCSS.HSF-BF.B.4A

Simplify the expression: $3^{\log_32x}$  

•  $2x$  

•  $-2x$  

•  $3x$  

•  $-3x$  

Find the inverse of the function f(x)=log₃(x)+7

• f^-1(x)=3^x-7

• f^-1(x)=3^(x+7)

• f^-1(x)=3^(x-7)

• f^-1(x)=3^x+7

Tags

CCSS.HSF-BF.B.4A

Find the inverse of  $y=6^x+3$  
Hint: Don't forget to isolate the exponential first.

• y=log₆(x+3)

• y=log₆(x-3)

• y=log₃(x-6)

• y=log₃(x+6)

Tags

CCSS.HSF-BF.B.4A

Find the inverse of  $y=4\left(5\right)^x$  

•  $y=\log_5\left(\frac{x}{4}\right)$  

•  $y=\log_5\left(\frac{4}{x}\right)$  

•  $y=\log_4\left(\frac{x}{5}\right)$  

•  $y=\log_4\left(\frac{5}{x}\right)$  

Tags

CCSS.HSF-BF.B.4A

Find the inverse: $y=2\left(4\right)^{x-7}$  

•  $y^{-1}=\log_4\left(\frac{x}{2}\right)+7$  

•  $y^{-1}=\log_4\left(\frac{x}{2}\right)-7$  

•  $y^{-1}=\log_4\left(x\right)+7$  

•  $y^{-1}=\log_4\left(x\right)-7$  

Find the inverse of the function  $f\left(x\right)=3^{x+2}-1$  

• f^-1(x)=log₃(x+1)-2

• f^-1(x)=log₃(x-1)+2

• f^-1(x)=log₃(x+1)+2

• f^-1(x)=log₃(x)

Tags

CCSS.HSF-BF.B.4A

Find the inverse of  $y=e^x$  

•  $y=\log x$  

•  $y=\ln x$  

•  $y=10\log x$  

•  $y=\ln e$  

Tags

CCSS.HSF-BF.B.4A