Určete definiční obor funkcí a uveďte, zda jsou sudé nebo liché:

\( f(x) = \frac{x^2}{1 + x} \) asymptotes (x^2)/(1+x) , x = -10 to 10 <sagecell> plot( (x^2)/(1+x), (x, -10, 10) )</sagecell>

\( f(x) = \sqrt{3x − x^3} \) plot sqrt(3x - x^3) , x = -10 to 10

\( f(x) = (x − 2) \sqrt{\frac{1 + x}{1 - x}} \) plot (x − 2) / sqrt((1 + x)/(1 - x)) , x=-10 to 10

\( f(x) =\ln(x^2 − 4) \) plot ln(x^2 − 4)

\( f(x) =\ln(x + 2) + ln(x − 2) \) plot ln(x + 2) + ln(x − 2)

\( f(x) =\ln(1 − 4x^2) \) plot ln(1 - 4x^2)

\( f(x) = \sqrt{3x^2 − 4x + 1} \) plot sqrt(3x^2 − 4x + 1)

\( f(x) =\ln \pi/x + \arctan 2x \) plot ln pi/x + arctg 2x

\( f(x) = \frac{\sqrt{x}}{\ln(2 - x)} \) plot sqrt(x)/( ln(2 - x))

\( f (x) = ln(x^2 + 5x + 10) \) plot ln(x^2 + 5x + 10) , x= -10 to 10

\( f(x) = 3x − x^3 \) plot 3x − x^3 , x=-10 to 10

\( f(x) = \sqrt[3]{(1-x)^2} + \sqrt[3]{(1+x)^2} \) plot cuberoot(1-x)^2 + cuberoot(1+x)^2

\( f(x) = a^x + a^{−x}, (a > 0) \) plot a^x + a^−x, a=1

\( f(x) = \ln \frac{1 - x}{1 + x} \) plot ln (1 - x)/(1 + x)

\( f(x) =\ln(x + \sqrt{1 + x^2} ) \) plot ln(x + sqrt(1 + x^2) )