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konrad509
[tex]f(g(x))=(2x^2+5)^2+2x^2+5+2\\ f(g(x))=4x^4+20x^2+25+2x^2+7\\ f(g(x))=4x^4+22x^2+32 [/tex]

For given functions f(x) and g(x) the composite function f(g(x)) is [tex]f(g(x))=4x^4+22x^2+32[/tex]

What is function?

  • "It defines a relation between input values and output values."
  • "In function, for each input there is exactly one output."

What is composition of function?

  • "It is applying one function to the results of another."  
  • "It is written is [tex]\( f\circ g(x)=f(g(x))[/tex] "
  • "First apply function f, then apply function g on the result of function f "

For given question,

We have been given two functions,

[tex]f(x) = x^2 + x + 2,~g(x) = 2x^2 + 5.[/tex]

We need to find f(g(x))

This means we need to find composite function [tex]\( f\circ g(x)=f(g(x))[/tex]

We have, [tex]g(x) = 2x^2 + 5[/tex]

We find the value of f(x) for x = g(x)

[tex]f(g(x))\\\\=f(2x^2 + 5)\\\\=(2x^2 + 5)^2 + (2x^2 + 5) + 2\\\\=[(2x^2)^2+2(2x^2)(5)+5^2]+2x^2+5+2\\\\=[4x^4+20x^2+25]+2x^2+7\\\\=4x^4+20x^2+2x^2+25+7\\\\=4x^4+22x^2+32[/tex]

Therefore, for given functions f(x) and g(x) the composite function f(g(x)) is [tex]f(g(x))=4x^4+22x^2+32[/tex]

Learn more about composite function here:

https://brainly.com/question/20379727

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