The function \( f: (-\infty, \infty) \to (-\infty, 1) \), defined by \[ f(x) = \frac{2^x - 2^{-x}}{2^x + 2^{-x}}, \] is:
We analyze the function \( f(x) \) to determine its injectivity and surjectivity. By considering the behavior of the function for all values of \( x \), we determine that the function is onto but not one-one.
Final Answer: Onto but not one-one.
For the reaction, \[ H_2(g) + I_2(g) \rightleftharpoons 2HI(g) \] Attainment of equilibrium is predicted correctly by:
Match List - I with List - II:
List - I:
(A) \([ \text{MnBr}_4]^{2-}\)
(B) \([ \text{FeF}_6]^{3-}\)
(C) \([ \text{Co(C}_2\text{O}_4)_3]^{3-}\)
(D) \([ \text{Ni(CO)}_4]\)
List - II:
(I) d²sp³ diamagnetic
(II) sp²d² paramagnetic
(III) sp³ diamagnetic
(IV) sp³ paramagnetic