Module B Outcome 5&6 Inverses

 $f^{-1}\left(x\right)\ =\$  {(0,5), (2,4), (3,1), (8,3), (15,2)}

 $f^{-1}\left(x\right)=$  {(-1,-3), (-2,-15), (-3,-8),(-4,-2), (-5,0)}

 $f^{-1}\left(x\right)\ =\$  {(0,5), (5,0), (10,2), (15,4), (20,6)}

 $f^{-1}\left(x\right)=$  {(0,-5), (-2,-10), (-4,-15),(-6,-20), (-5,0)}

 $f^{-1}\left(x\right)=\ 3x$  

 $f^{-1}\left(x\right)=\frac{x}{3}$  

The domain of the linear Function is  $\left(-\infty,\infty\right)$  , the Range of the function is  $\left(-\infty,\infty\right)$ the y- intercept and x intercept is 0.

The domain of the Exponential Function is  $\left(-\infty,\infty\right)$  , the Range of the function is  $\left(-\infty,\infty\right)$ the y- intercept and x intercept is 0.

 $f^{-1}\left(9\right)=27$  

The inverse of g(x) is  $g^{-1}\left(x\right)=-\frac{3x}{2}+\frac{15}{2}$  

The inverse of g(x) is  $g^{-1}\left(x\right)=-\frac{3}{2}x-\frac{15}{2}$  

 $g\left(9\right)=-1$  

 $g^{-1}\left(7\right)=-3$  

The absolute Value inequality

The absolute Value inequality $\left|d-120\right|\ge4$ can be used to calculate the size CD that CD players will play.

The domain that represents the size of CD's that can be played is [116, 124]

The domain that represents the size of CD's that can be played is (116, 124)

 $j^{-1}\left(x\right)=\sqrt{x-5}+2$  

 $j^{-1}\left(x\right)=\sqrt{x+5}-2$  

 $j^{-1}\left(x\right)=-\sqrt{x-5}-2$  

 $j^{-1}\left(x\right)=-\sqrt{x-5}+2$  

If the domain of d(x) is restricted to  $x\ge-3$  the inverse is  $d^{-1}\left(x\right)=\sqrt{\frac{x+5}{2}}-3$  

If the domain of d(x) is restricted to  $x\le-3$   the inverse is  $d^{-1}\left(x\right)=\ -\sqrt{\frac{\left(x+5\right)}{2}}-3$  

If the domain of d(x) is restricted to  $x\le-3$  the inverse is  $d^{-1}\left(x\right)=\sqrt{\frac{x+5}{2}}-3$  

If the domain of d(x) is restricted to  $x\ge-3$   the inverse is  $d^{-1}\left(x\right)=\ -\sqrt{\frac{\left(x+5\right)}{2}}-3$  

 $h\left(3\right)=35.5$  

 $h^{-1}\left(7\right)=2$  

The range of g(x) is  $\left(-\infty,-7\right]$  

An increasing interval of function g(x) is  $\left[5,\infty\right)$  

The piecewise function of g(x)

  $2x-17\ \ \ \ x<5$ 

   $-2x\ +3\ \ \ \ x\ge5$  

The piecewise function of g(x)
 $-2x+3\ \ \ \ x\le5$ 

 $2x-17\ \ \ \ \ \ x>5$   

The function $d\left(m\right)=0.10m\ +1.50$ can be used to model the scenario such that d(m) represents the cost of the long distance call given the amount of time m minutes.

The inverse function $d^{-1}\left(m\right)=10m-15$ can be used to model the scenario such that $d^{-1}\left(m\right)$ represents the time in minutes and m represents the cost of the long distance call.

The inverse function $d^{-1}\left(m\right)=10m-15$ can be used to model the scenario such that $d^{-1}\left(m\right)$ represents the cost of the long distance call given the m minutes.

$d^{-1}\left(10\right)=85$ indicates that a $10 call last for 85 minutes.

$d^{-1}\left(10\right)=85$ indicates that a 10 minute call costs $85