Inverses of Log Functions (AP Pre-Cal)

Inverses of Log Functions

By Manly Hanley

Multiple Choice

What is the domain of the graph?

• (-∞,∞)
• (-2, ∞)
• (0,∞)
• (-∞,2)

Multiple Choice

What is the range of the graph?

• (-∞,∞)
• (-2, ∞)

• (0,∞)
• (-∞,2]

Multiple Choice

What is the domain of the graph $$y=\log_4\left(x+2\right)$$

• (-∞,∞)
• (-2, ∞)

• (0,∞)
• (-∞,2]

Multiple Choice

What is the range of the graph $$y=\log_4\left(x+2\right)$$

• (-∞,∞)
• [-2, ∞)

• (0,∞)
• (-∞,2]

Multiple Choice

What is the domain of the graph?

• (-∞,∞)
• (-2, ∞)
• (0,∞)
• (-∞,-2)

Multiple Choice

What is the range of the graph?

• (-∞,∞)
• [-2, ∞)

• (0,∞)

• (-∞,-2]

Multiple Choice

What is the domain of the graph

$$y=\log_2\left(x\right)-5$$

• (-∞,∞)
• (-2, ∞)
• (0,∞)
• (-∞,-2)

Multiple Choice

What is the range of the graph

$$y=\log_2\left(x\right)-5$$

• (-∞,∞)
• (-2, ∞)
• (0,∞)
• (-∞,-2)

Multiple Choice

What is the equation of the asymptote?

• x = -3

• x=3

• y= -3

• y=5

Multiple Choice

Find the Inverse of $$y\ =\ \log_4\left(x-1\right)$$

• $$y=x$$  

• $$y=\log_34^x$$  

• $$y=4^x+1$$  

• $$y=4^{x+1}$$  

Multiple Choice

$$Find\ the\ inverse\ of\ :\ y=\log_9x+4$$  
HINT: isolate the logarithm first.

• $$y=9^x+4$$  

• $$y=9^x-4$$  

• $$y=9^{\left(x-4\right)}$$  

• $$y=9^{\left(x+4\right)}$$  

Multiple Choice

Find the inverse of :

• f(x)^-1 = 7^x-9

• f(x)^-1 = 7^x - 9

• f(x)^-1 = 7^x+9

• f(x)^-1 = 7^x +9

Multiple Choice

Find the inverse of $$y=\ln\left(x+3\right)$$  

• $$y=e^x-3$$  

• $$y=e^{x-3}$$  

• $$y=e^x+3$$  

• $$y=e^{x+3}$$  

Multiple Choice

Find the inverse of $$y=\frac{1}{3}\log⁡(x+1)$$  

• $$f^{-1}\left(x\right)=\left(10\right)^{3x}-1$$

• $$f^{-1}\left(x\right)=\left(10\right)^{3x-1}$$

• $$f^{-1}\left(x\right)=\left(10\right)^{3x}-1$$

Multiple Choice

Find the inverse of $$f\left(x\right)=-3\log_8\left(-x-6\right)+12$$  

• $$f^{-1}\left(x\right)=-\left(8\right)^{-\frac{1}{3}x+4}-6$$  

• $$f^{-1}\left(x\right)=\left(6\right)^{-\frac{1}{3}x}+8$$  

• $$f^{-1}\left(x\right)=\left(8\right)^{\frac{1}{3}x+4}+6$$