Inverse of Square Root Functions

Inverse of Square Root Functions

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Graphing the Inverse

Solving for Inverses Algebraically

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Multiple Choice

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

Multiple Choice

Which is the inverse of the table?

Multiple Choice

What is the DOMAIN of the function?

• [-3, infinity)
•  [0, infinity)
• [3, inifinity)
• (-infinity, 0}

Multiple Choice

Find the inverse function of $$y=\sqrt{x+11}$$  

• $$y=x^2-11$$  

• $$y=x^2+11$$  

• $$y=\left(x+11\right)^2$$  

• $$y=\left(x-11\right)^2$$  

Multiple Choice

Find the inverse function of $$f\left(x\right)=\sqrt{x}-6$$  

• $$y=\left(x+6\right)^2$$  

• $$y=\left(x-6\right)^2$$  

• $$y=x^2+6$$  

• $$y=x^2+36$$  

Multiple Choice

Find the inverse of $$f\left(x\right)=\sqrt{x+2}+9$$  

• $$f\left(x\right)=\left(x-9\right)^2-2$$  

• $$f\left(x\right)=\left(x+9\right)^2+2$$  

• $$f\left(x\right)=\sqrt{x+9}+2$$  

• $$f\left(x\right)=\sqrt{x-9}-2$$  

Multiple Choice

Find the inverse function of $$y=\sqrt{5x}$$  

• $$y=\frac{1}{5}x^2$$  

• $$y=5x^2$$  

• $$y=10x^2$$  

• $$y=\sqrt{3x+1}$$  

Multiple Choice

When finding the inverse of a relation, 
1st you replace f(x) with y
2nd switch the x's and y's
What do you do next?

• solve for y
• replace y with f^-1(x)
• solve for x
• find the greatest common factor

Multiple Choice

What is the range of the function in this graph?

• (- ∞, 3]

• [3, ∞)

• (-∞, 0]

• [0,∞)

Multiple Choice

The domain of a square root function is $$\left[4,\infty\right)$$ .

What is the RANGE of the inverse?

• $$\left[-4,\infty\right)$$

• $$\left(-\infty\ ,4\right]$$

• $$\left[4,\infty\right)$$

• Cannot be determined

Multiple Choice

The inverse of the function f(x) is written as ...

• f ^-1(x)
• f ²(x)
• f '(x)
• f ⁺(x)

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

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)