If the graph of the function `f(x)=(a^x-1)/(x^n(a^x+1))` is symmetrical about the y-a xi s ,then n equals 2 (b) `2/3` (c) `1/4` (d) `1/3`

The graph of the function y= f (x) is symmetrical about the line x=2 then

Draw the graph of the function y=f(x)=tan^(-1)((1-x^(2))/(1+x^(2))) .

Draw the graph of the function y= f(x) = lim_(n to oo) (x^(2n)-1)/(x^(2n)+1) . Is this function same as the function g(x) = "sgn"(x^(2)-1) .

If R->R is an invertible function such that f(x) and f^-1(x) are symmetric about the line y=-x, then (a) f(x) is odd (b) f(x) and f^-1(x) may be symmetric (c) f(c) may not be odd (d) non of these

The function f(x)=x(x+4)e^(-x//2) has its local maxima at x=adot Then (a) a=2sqrt(2) (b) a=1-sqrt(3) (c) a=-1+sqrt(3) (d) a=-4

If f(x) is a real-valued function defined as f(x)=In (1-sinx), then the graph of f(x) is (A) symmetric about the line x =pi (B) symmetric about the y-axis (C) symmetric and the line x=(pi)/(2) (D) symmetric about the origin

If lim_(x->0)(x^n-sinx^n)/(x-sin^n x) is non-zero finite, then n must be equal to 4 (b) 1 (c) 2 (d) 3

The range of the function f(x)=(x^2+x+2)/(x^2+x+1),x in R , is (1,oo) (b) (1,(11)/7) (c) (1,7/3) (d) (1,7/5)

Let f be a differential function such that f(x)=f(2-x) and g(x)=f(1 +x) then (1) g(x) is an odd function (2) g(x) is an even function (3) graph of f(x) is symmetrical about the line x= 1 (4) f'(1)=0

A function y-f(x) has a second-order derivative f^(x)=6(x-1)dot It its graph passes through the point (2,1) and at that point tangent to the graph is y=3x-5, then the value of f(0) is 1 (b) -1 (c) 2 (d) 0