Suppose that f is differentiable on R. If f(0) = 1 and |f(x)| < 1 for all

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Suppose that f is differentiable on R. If f(0) = 1 and |fʹ(x)| < 1 for all x ∈ R, prove that |f(x)| < |x| + 1 for all ∈ R.
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