What is (f⋅g)(x)?f(x)=x3−4x+2

g(x)=x2+2



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(f⋅g)(x)=

The value of the composition of function ( f . g )( x ) = x⁵ - 2x³ + 2x² - 8x + 4

What is Composition of functions?

Evaluation of a function at the value of another function is known as Composition of function. A function composition is a process in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.

Given data ,

Let the first function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = x³ - 4x + 2

Let the second function be represented as g ( x )

Now , the value of g ( x ) is

g ( x ) = x² + 2

Now , the composition of function ( f . g ) ( x ) = f ( x ) . g ( x )

On simplifying , we get

The composition of function ( f . g ) ( x ) = ( x³ - 4x + 2 ) ( x² + 2 )

A = x³ ( x ² ) - 4x ( x )² + 2x² + 2x³ - 8x + 4

A = x⁵ - 4x³ + 2x² + 2x³ - 8x + 4

On further simplification , we get

A = x⁵ - 2x³ + 2x² - 8x + 4

Hence , the composition of function is A = x⁵ - 2x³ + 2x² - 8x + 4

To learn more about composition of function click :

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