Question
Mathematics
$\begin{array}{l}f\left(x\right)=4{x}^{2}+3x-2\\ \\ g\left(x\right)=6{x}^{3}-3{x}^{2}-4\\ \\ \text{Find}\left(f+g\right)\left(x\right)\end{array}${:[f(x)=4x^(2)+3x-2],[],[g(x)=6x^(3)-3x^(2)-4],[],[" Find "(f+g)(x)]:}
A. $\left(f+g\right)\left(x\right)=-6{x}^{3}+7{x}^{2}+3x+2$(f+g)(x)=-6x^(3)+7x^(2)+3x+2
B. $\left(f+g\right)\left(x\right)=10{x}^{3}-6$(f+g)(x)=10x^(3)-6
C. $\left(f+g\right)\left(x\right)=6{x}^{3}+{x}^{2}+3x-6$(f+g)(x)=6x^(3)+x^(2)+3x-6
D. $\left(f+g\right)\left(x\right)=6{x}^{3}+4{x}^{2}-6$(f+g)(x)=6x^(3)+4x^(2)-6
To calculate $\left(f+g\right)\left(x\right)$(f+g)(x), we need to find $f\left(x\right)+g\left(x\right)$f(x)+g(x):
$\begin{array}{rl}f\left(x\right)+g\left(x\right)& =\left(4{x}^{2}+3x-2\right)+\left(6{x}^{3}-3{x}^{2}-4\right)\\ \\ & =6{x}^{3}+4{x}^{2}+3x-2-4\\ \\ & =6{x}^{3}+4{x}^{2}+3x-6.\end{array}${:[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, $\left(f+g\right)\left(x\right)=\overline{)\mathbf{\text{(D)}}6{x}^{3}+4{x}^{2}-6}$(f+g)(x)=(D) 6x^(3)+4x^(2)-6.