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.

Graph of $y = f (x), 0 \leq x < 3$ is shown below:

Representation of f(x) in terms of the unit step function is given by

Answer:

Solution:

We have $f (x) = ⎩ ⎨ ⎧ x - 1 2 0 \leq x < 1 1 \leq x < 2 2 \leq x < 3$ using the definition of $u (x)$ , $f (x)$ can be represented as

$f (x) = x {u (x) - u (x - 1)} - {u (x - 1) - u (x - 2)} + 2 u (x - 2) = x {u (x) - u (x - 1)} - u (x - 1) + 3 u (x - 2) 0 \leq x < 3$

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

⏱ 2mℹ️ Source: QB

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