Algebra Examples

$f {(x)}^{- 1} = 4 x - 3$

Divide each term in $f x^{- 1} = 4 x - 3$ by $x^{- 1}$ and simplify.

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Divide each term in $f x^{- 1} = 4 x - 3$ by $x^{- 1}$ .

$\frac{f x^{- 1}}{x^{- 1}} = \frac{4 x}{x^{- 1}} + \frac{- 3}{x^{- 1}}$

Simplify the left side.

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Cancel the common factor of $x^{- 1}$ .

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Cancel the common factor.

$\frac{f x^{- 1}}{x^{- 1}} = \frac{4 x}{x^{- 1}} + \frac{- 3}{x^{- 1}}$

Divide $f$ by $1$ .

$f = \frac{4 x}{x^{- 1}} + \frac{- 3}{x^{- 1}}$

Simplify the right side.

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Simplify each term.

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Move $x^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$f = 4 x \cdot x + \frac{- 3}{x^{- 1}}$

Multiply $x$ by $x$ by adding the exponents.

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Move $x$ .

$f = 4 (x \cdot x) + \frac{- 3}{x^{- 1}}$

Multiply $x$ by $x$ .

$f = 4 x^{2} + \frac{- 3}{x^{- 1}}$

Move $x^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$f = 4 x^{2} - 3 x$

To rewrite as a function of $x$ , write the equation so that $f$ is by itself on one side of the equal sign and an expression involving only $x$ is on the other side.

$f (x) = 4 x^{2} - 3 x$