Question

Дано функции f(x)= √ x+1 и g (x) = x^ 2 - 2x. Задайте формулой функцию:
1)y = f (3x)
2)y = g (-x)
3)y = f (g (x))
4)y = g (f (x))
5)y = f (f (x))
6)y = g (g (x))

Answer 1

$f(x) = sqrt {x+1}, g(x) = x^2 -2x. \ \ 1) y = f(3x)=sqrt{3x+1}; \ 2) y = g(-x) = x^2 + 2x; \ 3) y = f(g(x))=sqrt{x^2-2x+1} = sqrt{(x-1)^2}=|x-1|; \ 4) y = g(f(x)) = (sqrt{x+1})^2 - 2sqrt{x+1} = x + 1 - 2sqrt{x+1}; \ 5) y = f(f(x))= sqrt{sqrt{x+1}+1}; \ 6) y = g(g(x)) = (x^2-2x)^2 - 2(x^2-2x) = x^4 - 4x^3 + 4 x^2 - 2x^2 +\ + 4x = x^4 - 4x^3 + 2 x^2 +4x.$