Let <math xmlns="http://www.w3.org/1998/Math/MathML"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo>+</mo> <mn>1</mn> </math> and <math xmlns="http://www.w3.org/1998/Math/MathML"> <mi>g</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>2</mn> <mi>x</mi> <mo>+</mo> <mn>1</mn> </math>. Find the composite function.

restgarnut

restgarnut

Answered question

2022-09-04

Let f ( x ) = x 2 + 1 and g ( x ) = 2 x + 1 Find the composite function ( f g ) ( x )

Answer & Explanation

mercuross8

mercuross8

Beginner2022-09-05Added 16 answers

Given that
( f g ) ( x ) = f [ g ( x ) ] = f ( 2 x + 1 ) = ( 2 x + 1 ) 2 + 1 = 4 x 2 + 1 + 4 x + 1 = 4 x 2 + 4 x + 2

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