If f(x)=sinx+cosx, g(x)=`x^(2)-1`, then g{f(x)} is invertible in the domain

If f(x)=sin x+cos x and g(x)=x^(2)-1 then g(f(x)) is invertible in the domain.

If f(x)=cosx+sinx and g(x)=x^(2)-1 , then g(f(x)) is injective in the interval

If f(x)=sinx" and "g(x)=sgn sinx , then g'(1) equals

If f(x)=x, g(x)=sinx, then int f(g(x))dx is equal to

If f(x)=x^2 and g(x)=x^2+1 then: (f@g)(x)=(g@f)(x)=

If f(x)=3x+1 and g(x)=x^(3)+2 then ((f+g)/(f*g))(0) is:

If f(x) = x , g (x) = sinx , then int f(g(x)) dx is equal to

For x in R ,f(x)=|log2-sinx| and g(x)=f(f(x)) , then (1) g is not differentiable at x=0 (2) g'(0)=cos(log2) (3) g'(0)=-cos(log2) (4) g is differentiable at x=0 and g'(0)=-sin(log2)