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1.Given f(x)-2x-11 find f^1(x)

2.Describe the transformation of the parent function f(x)  h(x)=-3f(x)

3.Let f(x)=x^2+7x+9. does an inverse function exist for the entire domain of the function? Explain.

 May 12, 2020
 #1
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1. We can write

 

y = -2x -11          get x by itself

y +11  = - 2x

[ y +11]  / -2  =  x

- [ y +11]  / 2  =  x       "swap"  x and y

- [x + 11]  / 2  =  y  =  f-1(x)

 

2. h(x)  vertically  "stretches"  f(x)  by a factor  of 3  and  the "-"  flips this over the x axis

See  the graph here : https://www.desmos.com/calculator/9fq01ty1j3

 

3. This  has an inverse  but  it will not be a function......

 

f(x)  = x^2 + 7x + 9    is a parabola  that turns upward.......thus.....it will not pass the horizontal line test  [ a horizontal line drrawn through the function will cut the function in more than one place......so....not one-to-one ]

 

So....if the original function is not  one-to-one , then it won't have an inverse over its entire domain

 

cool cool cool

 May 12, 2020

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