Question

Aratati ca urmatoarele functii sunt bijectii f:(0,+∞)--> (0,+∞),f(x)=1/x

Answer 1

Injectivitatea

f(x₁)=f(x₂)

$\frac{1}{x_1} =\frac{1}{x_2} \\\\x_1=x_2$⇒f injectiva

Surjectivitatea

f(x)=y

$\frac{1}{x} =y\\\\xy=1\\\\x=\frac{1}{y} \\\\y > 0\\\\\frac{1}{y} > 0\\\\x > 0$⇒ f surjectiva ⇒ f bijectiva