Respuesta :

Nayefx

Answer:

[tex] \huge \boxed{ \boxed {\sf \: a)49 {x}^{2} + 14x + 1}}[/tex]

Step-by-step explanation:

to understand this

you need to know about:

  • composition of function
  • PEMDAS

tips and formulas:

  • [tex](g \circ f)x \iff g(f(x))[/tex]

let's solve:

  1. [tex] \sf sustitute \: the \: value \: of \: f(x) \: to \: g(x) : \\ \sf (7x + 1 {)}^{2} [/tex]
  2. [tex] \sf use \: (a + b {)}^{2} = {a}^{2} + 2ab + {b}^{2} \: to \: simplify : \\ (7x {)}^{2} + 2.7x.1 + ( {1)}^{2} [/tex]
  3. [tex] \sf simplify : \\ 49 {x}^{2} + 14x + 1[/tex]

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[tex]\huge\underline{\tt{\red{Problem:}}}[/tex]

  • Given [tex] \tt{f(x) = 7x + 1}[/tex]and [tex] \tt{g(x) = {x}^{2} }[/tex]find, [tex] \tt{( \: g \: \: • \ \: f \: )(x)}[/tex].

[tex]\huge\underline{\tt{\red{Formula:}}}[/tex]

[tex] \tt{( \: g \: \: • \ \: f \: )(x)}[/tex].

[tex]\huge\underline{\tt{\red{Solution:}}}[/tex]

[tex]\quad\quad\quad\quad \tt{ ({x}^{2} )(7x + 1)}[/tex]

[tex]\quad\quad\quad\quad \tt{ ({x}^{2} )(7x) = 7{x}^{3} }[/tex]

[tex]\quad\quad\quad\quad \tt{ ({x}^{2} )( 1) = {x}^{2} }[/tex]

Let's add it.

[tex]\quad\quad\quad\quad \boxed{\tt{ {7x}^{3} + {x}^{2} }}[/tex]

[tex]\huge\underline{\tt{\red{Answer:}}}[/tex]

[tex]\huge \quad\quad \underline{\red{ \boxed{\tt{{7x}^{3} + {x}^{2} }}}}[/tex]

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✍︎ C.Rose❀

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