If \(f(x)={ x }^{ 3 }-\frac { 1 }{ { x }^{ 3 } } \), x \(\neq\) 0, then show that \(f(x)+f\left( \frac { 1 }{ x } \right) =0\)

If \(f(x)=\frac { x+1 }{ x-1 } \) ,x ≠ 0 then prove that f(f(x)) = x

Find the derivative of the following functions from first principle. log (x + 1)

If \(f\left( x \right) =\frac { 1 }{ 2x+1 } ,x> -\frac { 1 }{ 2 } \) then show that \(f\left( f\left( x \right) \right) =\frac { 2x+1 }{ 2x+3 } \)

Show that the function f(x) = 5x -3 is continous at x = +3

Evaluate \(\underset { h\rightarrow 0 }{ lim } \frac { \sqrt { x+h } -\sqrt { x } }{ h } \)

Differentiate (sec x -1) (sec x +1)

Differentiate \(\frac { { x }^{ 2 }cos\frac { \pi }{ 4 } }{ sinx } \)

If f(x) = log \(\frac{1+x}{1-x}\), 0 < x < 1, then show that \(f(\frac{2x}{1+x^2})=2f(x)\).

If f(x) = x and g(x) = |x|, then find (f + g)(x)