Define derivative of a function 'f' at x = c

Define the continuity of a function at a point within its domain of definition. The definition of a function is given below: f(x)={{:((1-cos5x)/(x^(2))," when "(xne0)),(k," when x = 0"):} Find the value of k for which f(x) is continuous at x = 0.

The function f(x) is defined in 0 le x le1, find the domain of definition of f(x^2)

The function f(x) is defined in 0 le x le1, find the domain of definition of f(2x-1)

Does the equation y = 2x-9 represent y as a function of x ? If so, find the domain of definition and range of the function.

Draw the graph of the function f(x) = "max"{x, x^(2)} and write its equivalent definition.

The function f(x) is defined in [0,1] . Find the domain of f(t a nx)dot

Find the domain of the function: f(x)=(sin^(-1)x)/x

The domain of the function f(x)=1/sqrt(|x|-x) is