Question

Составить сложные функции:

y1=f(g(x))

y2=g(f(x))

a) f(x)=cosx, g(x)=1/(x^2+1)
b) f(x)=x^2+x-1, g(x)=ctgx

Answer 1

а) f(x) = Cos x ,  g(x) = 1/(x² + 1)
y1 = f(g(x)) = Cos(1/(x² + 1))
y2= g(f(x)) = 1/(Cos²x + 1)
б) f(x) = x² + x - 1,   g(x) = Ctg x
y1 = f(g(x)) = Ctg²x + Ctg x -1
y2= g(f(x))= Ctg(x² + x -1)