If the functions `f(x)=x^(3)+e^(x//2) " and " g(x)=f^(-1)(x)`, the value of g'(1) is ………… .

If f(x) = x^2 and g (x) = 2x + 3 , then the value of gof (-1) is

If f (x)= x^2 and g (x) =2x + 3 , then the value of gof(-1) is:

Suppose f(x) and g(x) are two continuous functions defined for 0<=x<=1 .Given, f(x)=int_0^1 e^(x+1) .f(t) dt and g(x)=int_0^1 e^(x+1) *g(t) dt+x The value of f( 1) equals

f(x)={(x-1",",-1 le x le 0),(x^(2)",",0le x le 1):} and g(x)=sinx Consider the functions h_(1)(x)=f(|g(x)|) and h_(2)(x)=|f(g(x))|. Which of the following is not true about h_(1)(x) ?

Let f_(1) (x) and f_(2) (x) be twice differentiable functions where F(x)= f_(1) (x) + f_(2) (x) and G(x) = f_(1)(x) - f_(2)(x), AA x in R, f_(1) (0) = 2 and f_(2)(0)=1. "If" f'_(1)(x) = f_(2) (x) and f'_(2) (x) = f_(1) (x) , AA x in R then the number of solutions of the equation (F(x))^(2) =(9x^(4))/(G(x)) is...... .

If the function f and g are defined as f(x)=e^(x) and g(x)=3x-2, where f:R rarr R and g:R rarr R , find the function fog and gof.

Which of the following pairs of function are identical? a. f(x)=e^(In sec^(-1)x) " and " g(x)=sec^(-1)x b. f(x)=tan(tan^(-1)x) " and " g(x)=cot(cot^(-1)x) c. f(x)=sgn(x) and g(x)=sgn(sgn(x)) d. f(x)=cot^(2)*cos^(2)x " and " g(x)=cot^(2)x-cos^(2)x

If f ( x) = cos^(-1) ( cos ( x + 1) ) " and " g(x) = sin ^(-1) ( sin (x + 2)) , then f(1) + g (1) = ( pi -1) f (1) gt g(1) f(2) gt g (2) f(2) lt g (2)

Let f and g be two functions defined by f(x) = sqrt(x-1) and g(x)= sqrt (4-x^2) . Find : g - f .

Let f(x)=x^2+xg'(1)+g''(2) and g(x)=f(1).x^2+xf'(x)+f''(x), then find f(x) and g(x).