First slide

Functions (XII)

Question

The domain of real valued function f(x)= $\sqrt{5 - 4 x - x^{2}}$ + $x^{2} + \log (x + 4)$ is

Moderate

A

-5 $\leq x \leq 1$
B

$- 5 \leq x a n d x \geq 1$
C

$- 4 < x \leq 1$
D

$ϕ$

Solution

Given f(x)= $\sqrt{5 - 4 x - x^{2}}$ + $x^{2} + \log (x + 4)$
$\Rightarrow 5 - 4 x - x^{2} \geq 0 a n d x + 4 > 0 \Rightarrow x^{2} + 4 x - 5 \leq 0 a n d x > - 4 \Rightarrow (x + 5) (x - 1) \leq 0 a n d x > - 4 \Rightarrow x \in [- 5, 1] a n d x > - 4 x \in (- 4, 1]$
or -4 $<$ x $\leq$ 1

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