Mathematics - Functions Question with Solution | TestHub

MathematicsFunctionsGeneral (Definition,type and special type)Medium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

The unit step function $u (x - a)$ is defined as:

$u (x - a) = {0, 1, x < a x \geq a$

The graph of $y = u (x - a)$ is as shown below. The domain of $u (x - a)$ is $R$ and its range is ${0, 1}$ .

Answer the following questions.

Let $f (x) = [x] 0 \leq x < 3$ where [ ] denotes the greatest integer function. The representation of $f (x)$ in terms of unit step function is

Answer:

Solution:

Using the definition of $u (x)$ , we can write $f (x)$ as $f (x) = u (x - 1) + u (x - 2) + u (x - 3), 0 \leq x < 3$ .

Stream:JEESubject:MathematicsTopic:FunctionsSubtopic:General (Definition,type and special type)

⏱ 2mℹ️ Source: QB

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