If f(x)=1/2[3^x+3^-x], g(x)=1/2[3^x-3^-x], then f(x) g(y)+f(y)g(x)=

The domain of log₁₀ (x³-x) is

The domain of 1/√[x]²-[x]-6 is

Let f be an injective function with domain{x, y ,z} and range {1,2,3}such that exactly one of the  following statements is correct and the remaining are false.

F(x)=1, f(y)≠1, f(z)≠2. The value of f¹(1) is

log (x+√x²+1)/x is

If f(x)=log (x-5)(2-x), g(x)=log (x-5), h(x)= log (2-x) then

The domain of Cos^-1(2x-3)+√9-4x² is

The domain of f(x)=^(9-x)P_x-4 is

The inverse of f(x)=10^x-10^-x/ 10^x+10^-x is

if f(x)=a^2x-a^-2x/a^2x+a^-2x, then f(x) is