Question

Здравствуйте! Подскажите, пожалуйста, чему равен g(x)?

f(x+1) = 1/x+2; f(g(x)) = 2/2x+2

Answer 1

Ответ:

$f(x+1) = \frac{1}{x + 2}\\f(x) = \frac{1}{x + 1}\\f(g(x)) = \frac{1}{g(x)+1} = \frac{1}{2x + 2}\\g(x) + 1 = 2x + 2\\g(x) = 2x + 1$

Answer 2

Ответ:

$f(x+1)=\dfrac{1}{x+2}\ \ ;\ \ \ f(g(x))=\dfrac{2}{2x+2}\\\\\\t=x+1\ \ \to \ \ \ x=t-1\ \ \to \ \ \ f(t)=\dfrac{1}{(t-1)+2}=\dfrac{1}{t+1}\ \ \ \to \\\\\\f(g(x))=\dfrac{1}{g(x)+1}=\dfrac{2}{2x+2}\ \ \ \to \ \ \ 2x+2=2\cdot (g(x)+1)\ \ |:2\ ,\\\\\\x+1=g(x)+1\\\\g(x)=x+1-1\\\\g(x)=x$