Solve {l}{f(x)=9x+3x^2-x^2}{(x)=-1}

$$\left. \begin{array} { l } { f ( x ) = 9 x + 3 x ^ { 2 } - x ^ { 2 } } \\ { ( x ) = - 1 } \end{array} \right.$$

Solve for f, x

$$x=-1$$

$$f=7$$

Solution Steps

Consider the first equation. Insert the known values of variables into the equation.

$$f\left(-1\right)=9\left(-1\right)+3\left(-1\right)^{2}-\left(-1\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$f\left(-1\right)=9\left(-1\right)+3\left(-1\right)^{2}+\left(-1\right)^{3}$$

Multiply 9 and -1 to get -9.

$$f\left(-1\right)=-9+3\left(-1\right)^{2}+\left(-1\right)^{3}$$

Calculate -1 to the power of 2 and get 1.

$$f\left(-1\right)=-9+3\times 1+\left(-1\right)^{3}$$

Multiply 3 and 1 to get 3.

$$f\left(-1\right)=-9+3+\left(-1\right)^{3}$$

Add -9 and 3 to get -6.

$$f\left(-1\right)=-6+\left(-1\right)^{3}$$

Calculate -1 to the power of 3 and get -1.

$$f\left(-1\right)=-6-1$$

Subtract 1 from -6 to get -7.

$$f\left(-1\right)=-7$$

Divide both sides by -1.

$$f=\frac{-7}{-1}$$

Fraction \frac{-7}{-1} can be simplified to 7 by removing the negative sign from both the numerator and the denominator.

$$f=7$$

The system is now solved.

$$f=7 x=-1$$