Question: Show that the function is continuous only at x = 0. (Assume that k is any nonzero real number.) f(x) [0, if x is rational

Show that the function

f(x) [0, if x is rational kx, if x is irrationalis continuous only at x = 0. (Assume that k is any nonzero real number.)

f(x) [0, if x is rational kx, if x is irrational

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