Show that the function f defined by f(x) = |1 – x + | x | |, where x is any real number, is a continuous function.

Question

TextAlgebra of Continuous Functions

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Show that every polynomial function is continuous.

Prove that every rational function is continuous.

Discuss the continuity of sine function.

TextAlgebra of Continuous Functions

Prove that the function defined by f(x) = tan x is a continuous function.

Show that the function defined by f(x) = sin (x2) is a continuous function.

Discuss the continuity of the cosine, cosecant, secant and cotangent functions.