Question

Detreminati domeniul mde definitie al functiei : f:D cu valori in R :
f(x)= log in baza 3 (2x-5), f(x)= radical din x patrat-2x-3, f(x)=arcsin x-1 supra x+1.

Answer 1

[tex]f(x)= log_{3} (2x-5) [/tex]
2x-5>0
2x>5
x>$\frac{5}{2}$
⇒ D∈($\frac{5}{2}$; + infinit)

f(x)=$\sqrt{ x^{2} -2x-3}$
$x^{2} -2x-3 \geq 0$
Δ=4+12=16
$x_{1} = \frac{2-4}{2} =-1$
$x_{2} = \frac{2+4}{2} =3$
faci tabelul semnului si ⇒ D∈(-infinit;-1]U[3;+infinit)

f(x)=arcsin$\frac{x-1}{x+1}$
-1≤$\frac{x-1}{x+1}$≤1
x+1≠0 ⇒ x≠-1