Consider two functions, f(x) and g(x) defined as under: `f(x)={1+x^3,x < 0 and g(x) ={(x-1)^(1/3) (x+1)^(1/2), x < 0.` Evaluate g(f(x)).

Consider the function f (x) and g (x), both defined from R to R f (x) = (x ^(3))/(2 )+1 -x int _(0)^(x) g (t) dt and g (x) =x - int _(0) ^(1) f (t) dt, then The number of points of intersection of f (x) and g (x) is/are:

Consider the functions f(x) and g(x), both defined from R rarrR and are defined as f(x)=2x-x^(2) and g(x)=x^(n) where n in N . If the area between f(x) and g(x) is 1/2, then the value of n is

Consider the functions f(x) and g(x), both defined from R rarrR and are defined as f(x)=2x-x^(2) and g(x)=x^(n) where n in N . If the area between f(x) and g(x) is 1/2, then the value of n is

Consider the function f(x) = |x^(3) + 1| . Then,

If the functions f(x) and g(x) are defined on R -> R such that f(x)={0, x in retional and x, x in irrational ; g(x)={0, x in irratinal and x,x in rational then (f-g)(x) is

Consider a function f:R rarr R defined by f(x)=x^(3)+4x+5 , then

If the functions of f and g are defined by f(x)=3x-4 and g(x)=2+3x then g^(-1)(f^(-1)(5))

consider the function f(x)=(x^(2))/(x^(2)-1) If f is defined from R-(-1,1)rarrR then f is

Consider the function f(x)=tan^(-1){(3x-2)/(3+2x)}, AA x ge 0. If g(x) is the inverse function of f(x) , then the value of g'((pi)/(4)) is equal to

When f: R to R and g: R to R are two functions defined by f(x) = 8x^(3) and g(x) = = x^((1)/(3)) respectively and (g of ) (x) = k (f o g ) (x) , then k is