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it is a question in my book said

Prove that the function [tex]f(x) = 2 + x - \tan ^{-1} x [/tex] has the property [tex]\mid f'(x)\mid < 1 [/tex]

Prove that f dose not have a fixed point

but i found that this function has a fixed point

[tex] y = 2 + y - \tan ^{-1} y [/tex]

[tex]y = \tan 2 [/tex]

is it right that the question is wrong

Prove that the function [tex]f(x) = 2 + x - \tan ^{-1} x [/tex] has the property [tex]\mid f'(x)\mid < 1 [/tex]

Prove that f dose not have a fixed point

but i found that this function has a fixed point

[tex] y = 2 + y - \tan ^{-1} y [/tex]

[tex]y = \tan 2 [/tex]

is it right that the question is wrong

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