Question

For the shift operator E, if f(x) = x2 and h = 1, then Ef(x) =​

Answer 1

Answer:

For the shift operator E, if f(x) = x2 and h = 1, then Ef(x) =

Answer 2

For the shift operator E, if f(x) = x² and h = 1, then Ef(x) = x² + 2x + 1

Given :

f(x) = x² and h = 1

To find :

The value of Ef(x) for the shift operator E

Solution :

Step 1 of 2 :

Write down the given function

Here the given function is

f(x) = x² and h = 1

Step 2 of 2 :

Find the value of Ef(x)

By definition of shift operator E

Ef(x) = f(x + h)

Thus we get

$\displaystyle \sf{ Ef(x) }$

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

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

$\displaystyle \sf{ = {(x + 1)}^{2} }$

$\displaystyle \sf{ = {x}^{2} + 2x + 1 }$