Let `f(x)=x^(2), x in R. " for any " A subseteq R,` define `g(A)={x in R: f(x) in A}`. If ` S=[0,4],` then which one of the following statements is not ture? (A) `f(g(S))=S` (B) `g(f(S)) ne S` (C) `g(f(S)) =g(S)` (D) `f(g(S))ne f(S)`

Let f : R ->R defined by f(x) = min(|x|, 1-|x|) , then which of the following hold(s) good ?

Let f : R ^(+) to R defined as f (x)= e ^(x) + ln x and g = f ^(-1) then correct statement (s) is/are:

Let f : R ^(+) to R defined as f (x)= e ^(x) + ln x and g = f ^(-1) then correct statement (s) is/are:

Let f= R rarr R and g: R rarr R defined by f(x)=x+1,g(x)=2x-3 .Find (f+g)(x) and (f-g)(x) .

Let f : R to R : f (x) =x^(2) " and " g: R to R : g (x) = (x+1) Show that (g o f) ne (f o g)

Let f: R->R and g: R->R be two non-constant differentiable functions. If f^(prime)(x)=(e^((f(x)-g(x))))g^(prime)(x) for all x in R , and f(1)=g(2)=1 , then which of the following statement(s) is (are) TRUE? f(2) 1-(log)_e2 (c) g(1)>1-(log)_e2 (d) g(1)<1-(log)_e2

Let f: R->R and g: R->R be two non-constant differentiable functions. If f^(prime)(x)=(e^((f(x)-g(x))))g^(prime)(x) for all x in R , and f(1)=g(2)=1 , then which of the following statement(s) is (are) TRUE? f(2) 1-(log)_e2 (c) g(1)>1-(log)_e2 (d) g(1)<1-(log)_e2

Let f: R->R and g: R->R be two non-constant differentiable functions. If f^(prime)(x)=(e^((f(x)-g(x))))g^(prime)(x) for all x in R , and f(1)=g(2)=1 , then which of the following statement(s) is (are) TRUE? f(2) 1-(log)_e2 (c) g(1)>1-(log)_e2 (d) g(1)<1-(log)_e2

If f: R to R and g: R to R are defined by f(x) =x-[x] and g(x) =[x] AA x in R, f(g(x)) =