Let f be a function with domain -3-5- and let g x -3 x -4- Then the domain of fog x is-A- -3- 1-3-B- -3- 1-3C- -3- 1-3D- None of these

The correct option is A [ 3, 1/3](fog)(x) = f[g(x)] = f(|3x + 4|). Since the domain of f is [ 3, 5], ∴ 3 ≤ |3x + 4| ≤ 5 ∴ 0 ≤ |3x + 4| ≤ 5 ⇒ |3x+4| ≤ 5 ⇒ 5 ≤ ...

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Let f be a fu...

Question

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

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

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

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

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Solution

The correct option is B $[- 3, \frac{1}{3}]$
(fog)(x) = f[g(x)] = f(|3x + 4|).
Since the domain of f is [-3, 5],
$∴ - 3 \leq | 3 x + 4 | \leq 5$
$∴ 0 \leq | 3 x + 4 | \leq 5$
$\Rightarrow | 3 x + 4 | \leq 5 \Rightarrow - 5 \leq 3 x + 4 \leq 5$
$\Rightarrow - 9 \leq 3 x \leq 1 \Rightarrow - 3 \leq x \leq \frac{1}{3}$ .
$∴$ Domain of fog is $[- 3, \frac{1}{3}]$

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

The correct option is B [−3,13](fog)(x) = f[g(x)] = f(|3x + 4|). Since the domain of f is [-3, 5], ∴−3≤|3x+4|≤5 ∴0≤|3x+4|≤5 ⇒|3x+4|≤5⇒−5≤3x+4≤5 ⇒−9≤3x≤1⇒−3≤x≤13. ∴ Domain of fog is [−3,13]