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1. If the domain of the function log x^2 is x < a or x > b, for some a and b, find a + b.

 

2. When the graph of y = 2x^2 - x + 7 is shifted four units to the right, we obtain the graph of y = ax^2 + bx + c. Find a + b + c.

 

3. If f(x)=x^3 + 3x^2 + 3x + 1, find \(f(f^{-1}(2010))\).

 

I could really use some help and the steps that it took to get to these answers! Thank you.

 Mar 22, 2019
 #1
avatar+103789 
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1. If the domain of the function log x^2 is x < a or x > b, for some a and b, find a + b.

 

We cannot take the log of  0  or a negative number

 

Thus.....x^2   must be positive.....so....    x  can be <  0    or > 0

 

So....

 

a + b  =   0

 

 

cool cool cool

 Mar 22, 2019
 #4
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0

Thank you very much!

Guest Mar 23, 2019
 #2
avatar+103789 
0

2. When the graph of y = 2x^2 - x + 7 is shifted four units to the right, we obtain the graph of y = ax^2 + bx + c. Find a + b + c.

 

 

Translating the graph  four units to the right  produces

 

2(x - 4)^2   - (x - 4)  +  7         =

 

2 ( x^2 - 8x + 16)  - x + 4  + 7  =

 

2x^2 - 16x + 32 - x + 11   =

 

2x^2 - 17x + 43

 

a + b + c   =    2  + (-17) + 43    =  28

 

 

cool cool cool

 Mar 22, 2019
 #3
avatar+103789 
0

3. If f(x)=x^3 + 3x^2 + 3x + 1, find   f (f-1 (2010) )

 

Not as tough as you might think

 

f ( f-1 (2010) )    =   2010     !!!

 

 

 

cool cool cool

 Mar 22, 2019

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