First slide

Functions (XII)

Question

The range of $f (x) = \log_{3} (5 - 4 x - x^{2})$ is

Moderate

A

$(- \infty, 2]$
B

$(- \infty, 2)$
C

$(- \infty, 4)$
D

$(- \infty, 3)$

Solution

$\begin{array}{r} f (x) = \log_{3} (5 - 4 x - x^{2}) = \log_{3} \{9 - (x - 2)^{2}\} \\ f (x) is defined if \\ \begin{aligned} 9 - (x - 2)^{2} > 0 but 9 - (x - 2)^{2} \leq 9 \\ or 0 < 9 - (x - 2)^{2} \leq 9 \\ or - \infty < \log_{3} \{9 - (x - 2)^{2}\} \leq \log_{3} 9 \end{aligned} \end{array}$
$Hence, the range is (- \infty, 2] .$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App