Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.7 Derivatives And Integrals Involving Inverse Trigonometric Functions - Exercises Set 6.7 - Page 470: 51

False.

$sin^{-1}(sin(x))$ is equal to $x$ on the interval $[-1,1]$, but other real numbers outside of this interval are not equal to $x$. Graph the equation on a graphing calculator to observe that the range of values only exist between $y=-1$ and $y=1$.