Question

If $f(x)= (2021^{2021} - x^{2021}$ then find the value of $f(f(2020))$.

Answer 1

Answer:

Required value is { ${2021}^{2021} - { ({ {2021}^{2021} - {2020}^{2021} })}^{2021}$}

Step-by-step explanation:

Given,

$f(x) = {2021}^{2021} - {x}^{2021}$

Here we want to find $ff(2020)$

Now,we are putting x=2020 and get

$f(2020) = {2021}^{2021} - {2020}^{2021}$

Again we are putting $x = f(2020)$

and get,

$ff(2020)= {2021}^{2021} - {f(2020)}^{2021} = {2021}^{2021} - { ({ {2021}^{2021} - {2020}^{2021} })}^{2021}$

Required value is {${2021}^{2021} - { ({ {2021}^{2021} - {2020}^{2021} })}^{2021}$}

This is a problem of value putting.

By one example,we can understand this concept easily.

Let $g(y) = {y}^{2} + y$

We are putting y=3,

$g(3) = {3}^{2} + 3 = 9 + 3 = 12$

Answer 2

Concept

The property that every input is related to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. Let A & B be any two non-empty sets. Only when each element in A has one end and one image in B will the mapping from A to B be a function.

Given

f(x) = 2021²⁰²¹ - x²⁰²¹

Find

We have to find the value of f(f(2020)).

Solution

Now, f(2020) = 2021²⁰²¹ - 2020²⁰²¹.

Then f(f(2021) = f(2021²⁰²¹ - 2020²⁰²¹) = 2021²⁰²¹ - (2021²⁰²¹ - 2020²⁰²¹)²⁰²¹

Therefore, the value of f(f(2020)) is 2021²⁰²¹ - (2021²⁰²¹ - 2020²⁰²¹)²⁰²¹.

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