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in Composite Functions by (48.0k points)

If f : R → R, f(x) = cos (x + 2), justify whether f is inverse function or not.

1 Answer

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Best answer

Given function,

f : R → R, f(x) = cos (x + 2)

Putting x = 2π

f(2π) = cos (2π + 2) = cos (2)

Putting x = 0

f(0) = cos (0 + 2) = cos 2

Since, only one image is obtained for 0 and 2π, so function is not one-one. Hence, function is not one-one onto.

Hence, f-1 : R → R does not exist.

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