Question

if F(x) = 4x(square) + 3 cos x + x * sin x+1
show that is an even function​

Answer 1

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• Prove that the given function is an Even function

• What does it mean by Even Function? Even function is a where f( x ) = f( -x ) . Graphically described in Attached photo.

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$\dashrightarrow \: \: \sf \: f(x) = 4 {x}^{2} + 3 \cos(x) + x \sin(x) + 1$

• Checking for x = neg ( x )

$\dashrightarrow \: \: \sf \: f( - x) = 4 {( - x)}^{2} + 3 \cos( - x) + ( - x) \sin( - x) + 1$

$\dashrightarrow \: \: \sf \: f( - x) = 4 {x}^{2} + 3 \cos(x) + ( x) \sin( x) + 1$

• Hence we can clearly see f( x )= f( -x )

$\\ \\ \: \: \: \: \: \bf {hence ,\: \: f(x) \: \:is\:\: a \: \: even \: \: function}$