Đáp án:
\(a)f\left( x \right) = 2{x^7} - 4{x^4} + {x^3} - {x^2} - x + 5\)
Giải thích các bước giải:
\(\begin{array}{l}
a)f\left( x \right) = \left( {1 + 1} \right){x^7} + \left( { - 1 - 3} \right){x^4} + \left( {2 - 1} \right){x^3} - {x^2} - x + 5\\
= 2{x^7} - 4{x^4} + {x^3} - {x^2} - x + 5\\
g\left( x \right) = - 4{x^5} - 3{x^4} + {x^2} - x + 1\\
b)f\left( x \right) + g\left( x \right) = 2{x^7} - 4{x^4} + {x^3} - {x^2} - x + 5 - 4{x^5} - 3{x^4} + {x^2} - x + 1\\
= 2{x^7} - 4{x^5} - 7{x^4} + {x^3} - 2x + 6\\
f\left( x \right) - g\left( x \right) = 2{x^7} - 4{x^4} + {x^3} - {x^2} - x + 5 + 4{x^5} + 3{x^4} - {x^2} + x - 1\\
= 2{x^7} + 4{x^5} - {x^4} + {x^3} - 2{x^2} + 4\\
c)f\left( { - 1} \right) = 2.{\left( { - 1} \right)^7} - 4.{\left( { - 1} \right)^4} + {\left( { - 1} \right)^3} - {\left( { - 1} \right)^2} - \left( { - 1} \right) + 5\\
= - 2 - 4 - 1 - 1 + 1 + 5 = - 1\\
g\left( { - \dfrac{1}{2}} \right) = - 4.{\left( { - \dfrac{1}{2}} \right)^5} - 3.{\left( { - \dfrac{1}{2}} \right)^4} + {\left( { - \dfrac{1}{2}} \right)^2} - \left( { - \dfrac{1}{2}} \right) + 1\\
= \dfrac{{27}}{{16}}
\end{array}\)
