Match the following columns `f:R->(-oo, 0] and f(x)=ln(sqrt(1+x^4)-x^2)`

Which of the following statements is/are true? f:R-R,f(x)=log(x+sqrt(1+x^(2))) is an odd function

Which of the following functions is one-one ? (1)f:R->R defined as f(x)=e^(sgn x)+e^(x^2) (2) f:[-1,oo) ->(0,oo) defined by f(x)=e^(x^2+|x|) (3)f:[3,4]->[4,6] defined by f(x)=|x-1|+|x-2|+|x-3|+x-4| (4) f(x) =sqrt(ln(cos (sin x))

Which of the following functions is one-one ? (1)f:R->R defined as f(x)=e^(sgn x)+e^(x^2) (2) f:[-1,oo) ->(0,oo) defined by f(x)=e^(x^2+|x|) (3)f:[3,4]->[4,6] defined by f(x)=|x-1|+|x-2|+|x-3|+x-4| (4) f(x) =sqrt(ln(cos (sin x))

Which of the following functions is one-one ? (1)f:R->R defined as f(x)=e^(sgn x)+e^(x^2) (2) f:[-1,oo) ->(0,oo) defined by f(x)=e^(x^2+|x|) (3)f:[3,4]->[4,6] defined by f(x)=|x-1|+|x-2|+|x-3|+x-4| (4) f(x) =sqrt(ln(cos (sin x))

If f : R to R is defined by f(x) = {{:(x+4" for " x lt - 4),(3x+2" for " -4 le x then match the following columns and choose the correct answer. {:(,"column I",,"column II"),((A),f(-5)+f(-4),(1),14),((B),f(|f(-8)|),(2),4),((C ),f(f(-7))+f(3),(3),-11),((D),f(f(f(0)))+1,(4),-1),(,,(5),5),(,,(6),0):}

Suppose f and g are two functions such that f,g: R -> R f(x)=ln(1+sqrt(1+x^2)) and g(x)=ln(x+sqrt(1+x^2)) then find the value of xe^(g(x))f(1/x)+g'(x) at x=1

The domain of the function f:R rarr R defined by f(x)=sqrt(x^(2)-3x+2) is (-oo,a]uu[b,oo) then b-a

Which of the following functions is one-one? (1)f:R rarr R defined as f(x)=e^(sgnx)+e^(x^(2))(2)f:[-1,oo)rarr(0,oo) defined by f(x)=e^(x^(2)+|x|)(3)f:[3,4]rarr[4,6] defined f(x)=|x-1|+|x-2|+|x-3|+x-4| (4) f(x)=sqrt(ln(cos(sin x)))

The inverse of the function of f:R to R given by f(x)=log_(a) (x+sqrt(x^(2)+1)(a gt 0, a ne 1) is