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f ( x ) = 4 x 2 + 3 x − 2 g ( x ) = 6 x 3 − 3 x 2 − 4 Find ( f + g ) ( x ) {:[f(x)=4x^(2)+3x-2],[],[g(x)=6x^(3)-3x^(2)-4],[],[" Find "(f+g)(x)]:}
A. ( f + g ) ( x ) = − 6 x 3 + 7 x 2 + 3 x + 2 (f+g)(x)=-6x^(3)+7x^(2)+3x+2
B. ( f + g ) ( x ) = 10 x 3 − 6 (f+g)(x)=10x^(3)-6
C. ( f + g ) ( x ) = 6 x 3 + x 2 + 3 x − 6 (f+g)(x)=6x^(3)+x^(2)+3x-6
D. ( f + g ) ( x ) = 6 x 3 + 4 x 2 − 6 (f+g)(x)=6x^(3)+4x^(2)-6
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Best Answer
To calculate ( f + g ) ( x ) (f+g)(x), we need to find f ( x ) + g ( x ) f(x)+g(x):
f ( x ) + g ( x ) = ( 4 x 2 + 3 x − 2 ) + ( 6 x 3 − 3 x 2 − 4 ) = 6 x 3 + 4 x 2 + 3 x − 2 − 4 = 6 x 3 + 4 x 2 + 3 x − 6. {:[f(x)+g(x)=(4x^(2)+3x-2)+(6x^(3)-3x^(2)-4)],[],[=6x^(3)+4x^(2)+3x-2-4],[],[=6x^(3)+4x^(2)+3x-6.]:}
Hence, ( f + g ) ( x ) = (D) 6 x 3 + 4 x 2 − 6 (f+g)(x)=(D) 6x^(3)+4x^(2)-6.
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