Question

if f(x)=x²-1 and g(x)=(x+1)² then (gof)(x)=?​

Answer 1

Hope this answers the question

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

$\sf{ Let \: f : A \to B \: and \: g : B \to \: A \: be \: two \: given \: functions \: }$

$\sf{Then \: the \: function \: gof : B \to \: B \: is \: defined \: as}$

$\sf{ \: (gof)(x) = g(f(x))\: }$

GIVEN

$\sf{ f(x) = {x}^{2} - 1 \: }$

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

TO DETERMINE

$\sf{ \: (gof)(x) \: }$

CALCULATION

$\sf{ \: (gof)(x) \: }$

$\sf{ = g(f(x))\: }$

$\sf{ \: = g( {x}^{2} - 1)\: }$

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

$= \sf{{( {x}^{2} )}^{2} }$

$= \sf{ \: {x}^{4} }$

Hence

$\sf{ \: (gof)(x) = {x}^{4} \: }$

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LEARN MORE FROM BRAINLY

Let A={1,2,0,-1} B={1,3-1,-3} and

function f = A to B f(x) =px+q

If f={ (1,1),(2,3),(0,-1),(-1,-3)}

find the value of p & q

https://brainly.in/question/21617889