Question

'If 'f' is a linear function satisfying f[x + f(x)] = x + f(x), then f(5) can be equal to:

Options

• 25

• – 5

• 0

• None of these

Answer 1

– 5

Explanation:

Let f(x) = ax + b

⇒ f(x + ax + b) = ax + b + x

⇒ a² = 1 and b = 0

⇒ f(x) = x or f(x) = – x

f(x) = ± 5.