Sets, Relations & Functions Question - None

Question

●Ex. 16 If f : ℝ → A, where A = {x : −5 < x < 7} is defined by f(x) = x² − 5 and if f⁻¹(13) = {−c, c, −(c − 1), c(c − 1)}, the value of c is

Accepted Answer

Solution:

f⁻¹(13) = {x : f(x) = 13} = {x : x² − 5 = 13}

⟹ x² = 18 ⟹ x = ±3√2

So f⁻¹(13) = {−3√2, 3√2}

Given that f⁻¹(13) = {−c, c, −(c − 1), c(c − 1)}

Comparing, we have c = 3√2

∴ c = 3

Question: