Applying and analysing functions

What is the restricted domain of the cosine function in order to have an inverse cosine function?

• $\left[0,\pi\right]\ -\ \left\{\frac{\pi}{2}\right\}$

• $\left[0,\pi\right]$

• $\left[-1,1\right]$

• $\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$

The domain and range of a one-to-one function y=f(x), are given below in set builder notation. Give the domain of this function's inverse also in set-builder notation.

Domain: {x|-3 $\le$  x $<$  5}

Range: {y|y $>$  -2}

Mathematical Equivalence

ON

What are the domain and range of f^-1(x)?

• Domain: [2,∞). Range: [3,∞)

• Domain: [3,∞). Range: [2,∞)

• Domain: (3,∞). Range: (2,∞)

• Domain: (2, ∞). Range: (3, ∞)

Q5. The teacher will mirror a similar problem.  You will follow the same steps while working out your problem.

• $f^{-1}\left(x\right)=\frac{1}{3}\left(x+7\right)^3$

• $f^{-1}\left(x\right)=\frac{1}{3}x^3-7$

• $f^{-1}\left(x\right)=-3\left(x+7\right)^3$

For the following function to be a one-to-one function, x cannot be what values?

 $\left\{\left(20,\ 21\right),\left(21,\ 14\right),\ \left(110,112\right),\left(x,7\right)\right\}$  

•  $20,\ 21,\ 11$  

•  $20,\ 121,\ 110$  

•  $20,\ 21,\ 110$  

•  $12,\ 21,110$  

What is the domain and range of a standard inverse sine function?

• Domain: [0, 2] Range: [-π, π]

• Domain: [-π, π] Range: [-1, 1]

• Domain: [1, 2] Range: [0, π]

• Domain: [-1, 1] Range: [-π/2, π/2]

What is the inverse of the square root parent function? 

 $f\left(x\right)=\sqrt{x}$  

•  $f^{-1}\left(x\right)=x^2$  

•  $f^{-1}\left(x\right)=x$  

•  $f^{-1}\left(x\right)=\sqrt{x}$  

•  $f^{-1}\left(x\right)=x^3$  

Mathematical Equivalence

ON

Range of cos inverse function

• $\left[\pi,\ 2\pi\right]$

• $\left(0\ ,\ \pi\right)$

• $\left[0,\ \pi\right]$

• $\left[\frac{-\pi}{2},\frac{\pi}{2}\right]$