Question

Select the correct answer from given alternatives.

If f(x) =`1/(1 - x)`, then f{f[f(x)]} is

Options

• x – 1

• 1 – x

• x

• – x

Answer 1

x

Explanation;

f[f(x)] = `"f"(1/(1 - x))`

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

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

= `(x - 1)/x`

∴ f{f[f(x)]} = `"f"((x - 1)/x)`

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

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

= x