Question

IfE is a shift operator, then the value of E2(x), when h= 1 is. a)x b) x-1 c) x+1 d) x+2​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

If E is a shift operator, then the value of E²(x), when h = 1 is

a) x

b) x-1

c) x+1

d) x+2

CONCEPT TO BE IMPLEMENTED

If E is a shift operator and f(x) is a function then

$\sf{Ef(x) = f(x+h) }$

EVALUATION

Here it is given that

E is a shift operator and h = 1

We have to find the value of E²(x)

Now

$\sf{{E}^{2}(x) }$

$\sf{ = E.E(x) }$

$\sf{ = E(x + h) }$

$\sf{ = E(x + 1) }$

$\sf{ = (x + 1 + h) }$

$\sf{ = (x + 1 + 1) }$

$\sf{ = (x + 2) }$

FINAL ANSWER

Hence the correct option is d) x + 2

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