Question

запишите сложные функции f(g(x)) и g(f(x))
1)f(x)=x^2 и g(x)=2x-5
2)f(x)=x^2+1 и g(x)=√3-x
3)f(x)=x^2-1 и g(x)=x^2+1
4)f(x)=2/x и g(x)=x^2-3x+2
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Answer 1

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