Old nested functions. ^^ this but watch your parenthesis and signs when simplifying. As for b? I require a happy ending or a free wax. Your choice.Show off here.
First, f(g(x)) = (2x + p)^2 - 2.
Second g(f(x)) = 2 (x^2 - 2) + p.
Third ((2x + p)^2 - 2) - (2 (x^2 - 2) + p) can be expanded/simplified to the formula in the problem.
Someone else can hopefully help with b if you need more help from there.
As far as I can tell, part b turns into a quadratic mess, unless I'm missing something.
Edit, nevermind, the value for p should be (-2).
Thank youTo solve, use the quadratic function. We are only worried about the part under the square root, because that is what changes:
+/- root (b^2 - 4ac)
+/- root(16p^2 - 8*(p^2 - p +2) )
+/- root(8p^2 + 8p - 16)
Only time positive and negative roots are equal is when that is zero. Factor out and divide by 8.
p^2 + p - 2 = 0
(p+2)(p-1) = 0
p = (-2, 1)
After replacing back in, p=1 doesn't work. p=-2 does.