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Let

f(x) = x^2 - 4 if x >= -4

f(x) = 3x + 1 if x < -4

 

Then for how many values of x is f(f(x)) = 5?

 
 Jun 8, 2021
 #1
avatar+113569 
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solve f(x)=5

 

if x >= -4 

5 = x^2 - 4 

9=x^2

x= +3 or -3  but X>-4 so both are ok

 

Now solve  f(x)=3  and then f(x)=-3

3=x^2-4

7=x^2

x=+/- sqrt(7)   both are bigger than -4 so they are ok

 

-3=x^2-4

1=x^2

x=+1 or -1

 

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Solve f(x)=5 when  x<-4

5=3x+1

4=3x

x=4/3  which is not less than -4 so there are no solutions here

-----------

 

So I have found      x=sqrt(7), x=-sqrt(7), x=1 and x=-1

 

I have checked these answers, they all work.

 
 Jun 9, 2021

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