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Mathematics - Functions Question with Solution | TestHub

MathematicsFunctionsCompositeMedium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

Let $f (x) = {2 x + a b x^{2} + 3 : x \geq - 1 : x < - 1$ and $g (x) = {x + 4 - 3 x - 2 : 0 \leq x \leq 4 : - 2 < x < 0$ be functions.

If domain of $g (f (x))$ is [- 1, 4], then

Options:

Answer:

Solution:

$x \in [- 1, 2] \Rightarrow - 1 \leq x \leq 2 \Rightarrow - 2 \leq 2 x \leq 4 \Rightarrow - 2 + a \leq 2 x + a \leq 4 + a$ $\Rightarrow - 2 + a \leq - 2 and 4 + a \leq 4 i.e. a = 0$ B can take any value.

Stream:JEESubject:MathematicsTopic:FunctionsSubtopic:Composite

⏱ 2mℹ️ Source: QB

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