If possible, redefine the function to make it continuous f(x) = x^(1/x - 1), for x ≠ 1

Question

If possible, redefine the function to make it continuous.

\(f(x) = x^{(\frac{1}{x - 1})},\) for x ≠ 1

f(x) = x^{(1/x - 1),} for x ≠ 1

= e², for x = 1; at x = 1.

Answer 1

f(x) = x^{(1/x - 1)}

^{\(\therefore\)} f has removable discontinuity at x = 1

This discontinuity can be removed by redefining the function as: