Question

$$\left. \begin{array} { l l l l } { | c | c | c | c | c | c | c | } x & { - 6 } & { - 5 } & { - 4 } & { - 3 } & { - 2 } & { 0 } \\ f ( x ) = x ^ { 2 } + 6 x + 11 & { } & { } & { } & { 1 } & { 0 } \\ \end{array} \right.$$

Answer

$$f=(-(x^2+6*x+11)/21-6/7)/x$$

Solution


Simplify  \(-6-5-4-3-21fx\)  to  \(-21fx-18\).
\[-21fx-18={x}^{2}+6x+11\]
Factor out the common term \(3\).
\[-3(7fx+6)={x}^{2}+6x+11\]
Divide both sides by \(-3\).
\[7fx+6=-\frac{{x}^{2}+6x+11}{3}\]
Subtract \(6\) from both sides.
\[7fx=-\frac{{x}^{2}+6x+11}{3}-6\]
Divide both sides by \(7\).
\[fx=\frac{-\frac{{x}^{2}+6x+11}{3}-6}{7}\]
Simplify  \(\frac{-\frac{{x}^{2}+6x+11}{3}-6}{7}\)  to  \(-\frac{\frac{{x}^{2}+6x+11}{3}}{7}-\frac{6}{7}\).
\[fx=-\frac{\frac{{x}^{2}+6x+11}{3}}{7}-\frac{6}{7}\]
Simplify  \(\frac{\frac{{x}^{2}+6x+11}{3}}{7}\)  to  \(\frac{{x}^{2}+6x+11}{3\times 7}\).
\[fx=-\frac{{x}^{2}+6x+11}{3\times 7}-\frac{6}{7}\]
Simplify  \(3\times 7\)  to  \(21\).
\[fx=-\frac{{x}^{2}+6x+11}{21}-\frac{6}{7}\]
Divide both sides by \(x\).
\[f=\frac{-\frac{{x}^{2}+6x+11}{21}-\frac{6}{7}}{x}\]