Solve f(x)=3(2)^xtext{for}x=-1

$$f ( x ) = 3 ( 2 ) ^ { x } \text { for } x = - 1$$

Solve for f, x

$$x=-1$$

$$f = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Solution Steps

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

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

Calculate 2 to the power of -1 and get \frac{1}{2}.

$$f\left(-1\right)=3\times \frac{1}{2}$$

Multiply 3 and \frac{1}{2} to get \frac{3}{2}.

$$f\left(-1\right)=\frac{3}{2}$$

Divide both sides by -1.

$$f=\frac{\frac{3}{2}}{-1}$$

Express \frac{\frac{3}{2}}{-1} as a single fraction.

$$f=\frac{3}{2\left(-1\right)}$$

Multiply 2 and -1 to get -2.

$$f=\frac{3}{-2}$$

Fraction \frac{3}{-2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$f=-\frac{3}{2}$$

The system is now solved.

$$f=-\frac{3}{2} x=-1$$