Solve f(1/2)=(1/2)^3-4/(frac{1{2})}

$$f ( \frac { 1 } { 2 } ) = \frac { ( \frac { 1 } { 2 } ) ^ { 3 } - 4 } { ( \frac { 1 } { 2 } ) }$$

Evaluate

$$-\frac{31}{4}=-7.75$$

Solution Steps

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

$$\frac{\frac{1}{8}-4}{\frac{1}{2}}$$

Convert 4 to fraction \frac{32}{8}.

$$\frac{\frac{1}{8}-\frac{32}{8}}{\frac{1}{2}}$$

Since \frac{1}{8} and \frac{32}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1-32}{8}}{\frac{1}{2}}$$

Subtract 32 from 1 to get -31.

$$\frac{-\frac{31}{8}}{\frac{1}{2}}$$

Divide -\frac{31}{8} by \frac{1}{2} by multiplying -\frac{31}{8} by the reciprocal of \frac{1}{2}.

$$-\frac{31}{8}\times 2$$

Express -\frac{31}{8}\times 2 as a single fraction.

$$\frac{-31\times 2}{8}$$

Multiply -31 and 2 to get -62.

$$\frac{-62}{8}$$

Reduce the fraction \frac{-62}{8} to lowest terms by extracting and canceling out 2.

$$-\frac{31}{4}$$

Factor

$$-\frac{31}{4} = -7\frac{3}{4} = -7.75$$