Let be given by .

MATHEMATICS · Multi-part · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

Let

h: \mathbb R \to \mathbb R

be given by

h(x)=x+\sin x

. (i) Prove that

h

is injective on

\mathbb R

. (ii) Hence, or otherwise, solve

h(x)=h(y)

for real numbers

x

and

y

and interpret your result.

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