Two functions f(x) and g(x) are defined as f(x)= log 3|(x-2/x2-10 x+24)| and g(x)= sin - 1((2[x]-3/15)) then find the number of even integers for which ( f ( x )+ g ( x )) is defined. [Note: [k] denotes greatest integer less than or equal to k.]

Question

Two functions f(x) and g(x) are defined as f(x)= log 3|(x-2/x2-10 x+24)| and g(x)= sin - 1((2[x]-3/15)) then find the number of even integers for which ( f ( x )+ g ( x )) is defined. [Note: [k] denotes greatest integer less than or equal to k.] (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Domain =[-6,10)- 2,4,6 ∴ Even integers in the domain are -6,-4,-2,0,8

Q. Two functions f(x) and g(x) are defined as f(x)=log3​∣∣​x2−10x+24x−2​∣∣​ and g(x)=sin− 1(152[x]−3​) then find the number of even integers for which (f(x)+g(x)) is defined. [Note : [k] denotes greatest integer less than or equal to k.]

Domain =[−6,10)−{2,4,6} ∴ Even integers in the domain are −6,−4,−2,0,8

Domain $= [- 6, 10) - {2, 4, 6}$
$∴$ Even integers in the domain are $- 6, - 4, - 2, 0, 8$