SOLUTION: what is the answer for this solution... given g(x)=x²-16 find g(2x²); g(x²-3); g(x+h); g(x)+g(x); g(x+h)-g(x)?

g(x) = x² - 16 find 

g(2x²); 

Start with 

g(x) = x² - 16

Take out all the x's:

g( ) =  ² - 16

Put (2x²) where the x's were:

g(2x²) = (2x²)² - 16

Simplify the right side:

g(2x²) = 22x4 - 16 

g(2x²) = 4x4 - 16 

--------------------------------------------

g(x²-3)

Start with 

g(x) = x² - 16

Take out all the x's:

g( ) =  ² - 16

Put (x²-3) where the x's were:

g(x²-3) = (x²-3)² - 16

Simplify the right side:

g(x²-3) = (x²-3)(x²-3) - 16

g(x²-3) = x4 - 6x² + 9 - 16
 
g(x²-3) = x4 - 6x² - 7

--------------------------------------------

g(x+h); 

Start with 

g(x) = x² - 16

Take out all the x's:

g( ) =  ² - 16

Put (x+h) where the x's were:

g(x+h) = (x+h)² - 16

Simplify the right side:

g(x+h) = (x+h)(x+h) - 16

g(x+h) = x² + 2hx + h² - 16
 
-------------------------------------

g(x)+g(x); 

Add the equation g(x) = x² - 16 to itself:

            g(x) =  x² - 16
            g(x) =  x² - 16
            --------------
       g(x)+g(x) = 2x² - 32

------------------------------------

g(x+h)-g(x)

Write down the g(x+h) equation from above and the original
equation for g(x) under it, lining up the like terms:

          g(x+h) = x² + 2hx + h² - 16
            g(x) = x²            - 16

Now we multiply the second equation by -1, and add the two
term by terms:

          g(x+h) =  x² + 2hx + h² - 16
           -g(x) = -x²            + 16
       --------------------------------
     g(x+h)-g(x) =       2hx + h²

Edwin