Solve {l}{f(x)=-x^2+3}{x=-5/3}

$$\left. \begin{array} { l } { f ( x ) = - x ^ { 2 } + 3 } \\ { x = - \frac { 5 } { 3 } } \end{array} \right.$$

Solve for f, x

$$x = -\frac{5}{3} = -1\frac{2}{3} \approx -1.666666667$$

$$f=-\frac{2}{15}\approx -0.133333333$$

Solution Steps

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

$$f\left(-\frac{5}{3}\right)=-\left(-\frac{5}{3}\right)^{2}+3$$

Calculate -\frac{5}{3} to the power of 2 and get \frac{25}{9}.

$$f\left(-\frac{5}{3}\right)=-\frac{25}{9}+3$$

Add -\frac{25}{9} and 3 to get \frac{2}{9}.

$$f\left(-\frac{5}{3}\right)=\frac{2}{9}$$

Multiply both sides by -\frac{3}{5}, the reciprocal of -\frac{5}{3}.

$$f=\frac{2}{9}\left(-\frac{3}{5}\right)$$

Multiply \frac{2}{9} and -\frac{3}{5} to get -\frac{2}{15}.

$$f=-\frac{2}{15}$$

The system is now solved.

$$f=-\frac{2}{15} x=-\frac{5}{3}$$