Write as a Function of y y=1/x

$y = \frac{1}{x}$

Step 1

Rewrite the equation as $\frac{1}{x} = y$ .

$\frac{1}{x} = y$

Step 2

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x, 1$

The LCM of one and any expression is the expression.

$x$

Step 3

Multiply each term in $\frac{1}{x} = y$ by $x$ to eliminate the fractions.

Multiply each term in $\frac{1}{x} = y$ by $x$ .

$\frac{1}{x} x = y x$

Simplify the left side.

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{1}{x} x = y x$

Rewrite the expression.

$1 = y x$

Step 4

Solve the equation.

Rewrite the equation as $y x = 1$ .

$y x = 1$

Divide each term in $y x = 1$ by $y$ and simplify.

Divide each term in $y x = 1$ by $y$ .

$\frac{y x}{y} = \frac{1}{y}$

Simplify the left side.

Cancel the common factor of $y$ .

Cancel the common factor.

$\frac{y x}{y} = \frac{1}{y}$

Divide $x$ by $1$ .

$x = \frac{1}{y}$

Step 5

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

$f (y) = \frac{1}{y}$

Write as a Function of y y=1/x

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