91影视

The given functions are$f\left(x\right)=4x^2鈭�7x+3$and$g\left(x\right)=4x^2+2x鈭�1$

We find $鈸�(f+g)\left(x\right)鈸�(f+g)\left(2\right)鈸�(f鈭�g)\left(x\right)鈸�(f鈭�g)(鈭�3)$for the given function.

We find the value of $(f+g)\left(x\right)$for the given function.

We know$(f+g)\left(x\right)=f\left(x\right)+g\left(x\right)$

$(f+g)\left(x\right)=(4x^2-7x+3)+(4x^2+2x-1)$

Rewrite without the parentheses

$(f+g)\left(x\right)=4x^2-7x+3+4x^2+2x-1$

Put like terms together

$(f+g)\left(x\right)=4x^2+4x^2+2x-7x+3-1$

Combine like terms

$(f+g)\left(x\right)=8x^2-5x+2$

In part (a) we found $(f+g)\left(x\right)$and now we have to find $(f+g)\left(2\right)$.

To find $(f+g)\left(2\right)$we substitute $x=2$in the value of $(f+g)\left(x\right)$.

$(f+g)\left(x\right)=8x^2-5x+2$

put $x=2$

$$\begin{gathered} (f+g)\left(2\right)=8{\left(2\right)}^2-5路2+2 \\ (f+g)\left(2\right)=8路4-5路2+2 \\ (f+g)\left(2\right)=32-10+2 \\ (f+g)\left(2\right)=24 \end{gathered}$$

We find the value of$(f-g)\left(x\right)$for the given function.

We know$(f-g)\left(x\right)=f\left(x\right)-g\left(x\right)$

$(f-g)\left(x\right)=(4x^2-7x+3)-(4x^2+2x-1)$

Rewrite without the parentheses

$(f-g)\left(x\right)=4x^2-7x+3-4x^2-2x+1$

Put like terms together

$(f-g)\left(x\right)=4x^2-4x^2-2x-7x+3+1$

Combine like terms

$(f-g)\left(x\right)=-9x+4$

In part (c) we found $(f-g)\left(x\right)$now we have to find$(f-g)(-3)$

To find the value of$(f-g)(-3)$ we put $x=-3$in the value of$(f-g)\left(x\right)$

$(f-g)\left(x\right)=-9x+4$

put $x=-3$

$$\begin{gathered} (f-g)(-3)=-9(-3)+4 \\ (f-g)(-3)=27+4 \\ (f-g)(-3)=31 \end{gathered}$$