If possible, redefine the function to make it continuous f(x) = (x + x^2 + x^3 + x^4 - 4)/(x - 1), for x ≠ 1.

Question

If possible, redefine the function to make it continuous.

\(f(x) = \frac{x + x^2 + x^3 + x^4 - 4}{(x - 1)},\) for x ≠ 1.

f(x) = (x + x² + x³ + x⁴ - 4)/(x - 1), for x ≠ 1.

= 5, for x = 1; at x = 1.

Answer 1

f(x) = (x + x² + x³ + x⁴ - 4)/(x - 1)

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

This discontinuity can be removed by redefining the function as: