Question

If f(x) = `1/(1 - x)`, the number of points of discontinuity of f{f[f(x)]} is ______.

Options

• 2

• 1

• 0

• infinite

Answer 1

If f(x) = `1/(1 - x)`, the number of points of discontinuity of f{f[f(x)]} is 2.

Explanation:

f{f[f(x)]} = `f[f(1/(1 - x))]`

= `f(1/(1 - 1/(1 - x)))`

= `f((x - 1)/x)`

∴ f(x) is not defined for x = 1; `f(1/(1 - x))` is not defined for x = 0.

∴ f{f[f(x)]} is discontinuous at x = 0 and 1

i.e., there are two points of discontinuity.