Let f x = x 2 - x + 1 , ∀ x ≥ 1 2 , then the solution of the equation f x = f - 1 x is

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Question: Answered & Verified by Expert

Let

f (x) = x^{2} - x + 1, \forall x \geq \frac{1}{2},

then the solution of the equation

f (x) = f^{- 1} (x)

is

MathematicsFunctionsJEE Main

Options:

A $x =1$
B $x = 2$
C $x = \frac{1}{2}$
D $x = 3$

Solution:

1086 Upvotes Verified Answer

The correct answer is:

x =1

f (x) and f^{- 1} (x)

intersect only on the line

y = x

∴ x^{2} - x + 1 = x

\Rightarrow x^{2} - 2 x + 1 = 0

\Rightarrow {(x - 1)}^{2} = 0

\Rightarrow x = 1

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