Question

For the shift operator E, the value of E4f(x) =​

Answer 1

SOLUTION

TO DETERMINE

For the shift operator E, the value of

$\sf{ {E}^{4} f(x)}$

EVALUATION

We know that for an arbitrary function f(x) the shifting operator or shift operator E is defined as

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

Now

$\sf{ {E}^{4} f(x)}$

$\sf{ = {E}^{3}. Ef(x)}$

$\sf{ = {E}^{3} f(x + h)}$

$\sf{ = {E}^{2}. Ef(x + h)}$

$\sf{ = {E}^{2} f(x + 2h)}$

$\sf{ = {E}^{}. Ef(x + 2h)}$

$\sf{ = Ef(x + 3h)}$

$\sf{ = f(x + 4h)}$

FINAL ANSWER

$\sf{ {E}^{4} f(x) = f(x + 4h)}$

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