First slide

Functions (XII)

Question

Let f be a function with domain [–3, 5] and let g (x) = |3x + 4|. Then the domain of ( fog) (x) is

Moderate

A

$(- 3, \frac{1}{3})$
B

$[- 3, \frac{1}{3}]$
C

$[- 3, \frac{1}{3})$
D

None of these

Solution

Solution: (B)
( fog) (x) = f [g (x)] = f (|3x + 4|)
Since the domain of f is [–3, 5],
$∴$ –3 ≤ |3x + 4| ≤ 5 ⇒ |3x + 4|≤ 5
⇒ –5 ≤ 3x + 4 ≤ 5
⇒ –9 ≤ 3x ≤ 1
$\Rightarrow - 3 \leq x \leq \frac{1}{3}$
$∴$ Domain of fog is $[- 3, \frac{1}{3}]$

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