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.
+129849 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
+129849 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
