First slide

Functions (XII)

Question

Which of the following functions is bounded

Moderate

A

$y = 1 - \log_{10} x$
B

$y = e^{- 2 x}$
C

$y = \sin^{- 1} (2 x + 1)$
D

$y = \tan (4 x + 1)$

Solution

The range $\log_{10} x is (- \infty, \infty) so y = 1 - \log_{10} x$
is unbounded $y = e^{- 2 x}$ is unbounded from below as $x \to - \infty$ $y \to \infty$ . The range of $\sin^{- 1} x$ is $[\frac{- π}{2}, \frac{π}{2}]$ so $y = \sin^{- 1} (2 x + 1)$ is
a bounded function. The range of tan x is R so $y = \tan (4 x + 1)$ is unbounded

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