Set, Relation and FunctionHard

Question

If f(x) = ax + b (a < 0) is an onto function defined as f : [0, 1] → [0, 2], then cot

is equal to

Options

A.

B.

C.f(1)

D.

Solution

If f is onto and a < 0, then
f(0) = 2 ⇒ b = 2
f(1) = 0 ⇒ a + b = 0
a = - 2
∴ f(x) = - 2x + 2
Now, cot = 0
= f(1)

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