Graph f^-1(x)=-x/2+3/2

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

Step 1

Rewrite the function as an equation.

$y = - \frac{x}{2} + \frac{3}{2}$

Step 2

Rewrite in slope-intercept form.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Write in $y = m x + b$ form.

Reorder terms.

$y = - (\frac{1}{2} x) + \frac{3}{2}$

Remove parentheses.

$y = - \frac{1}{2} x + \frac{3}{2}$

Step 3

Use the slope-intercept form to find the slope and y-intercept.

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = - \frac{1}{2}$

$b = \frac{3}{2}$

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $- \frac{1}{2}$

y-intercept: $(0, \frac{3}{2})$

Slope: $- \frac{1}{2}$

y-intercept: $(0, \frac{3}{2})$

Step 4

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

Write in $y = m x + b$ form.

Reorder terms.

$y = - (\frac{1}{2} x) + \frac{3}{2}$

Remove parentheses.

$y = - \frac{1}{2} x + \frac{3}{2}$

Find the x-intercept.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = - \frac{1}{2} x + \frac{3}{2}$

Solve the equation.

Rewrite the equation as $- \frac{1}{2} x + \frac{3}{2} = 0$ .

$- \frac{1}{2} x + \frac{3}{2} = 0$

Combine $x$ and $\frac{1}{2}$ .

$- \frac{x}{2} + \frac{3}{2} = 0$

Subtract $\frac{3}{2}$ from both sides of the equation.

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

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- x = - 3$

Divide each term in $- x = - 3$ by $- 1$ and simplify.

Divide each term in $- x = - 3$ by $- 1$ .

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 3$ by $- 1$ .

$x = 3$

x-intercept(s) in point form.

x-intercept(s): $(3, 0)$

Find the y-intercept.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = - \frac{1}{2} \cdot 0 + \frac{3}{2}$

Solve the equation.

Remove parentheses.

$y = - \frac{1}{2} \cdot 0 + \frac{3}{2}$

Simplify $- \frac{1}{2} \cdot 0 + \frac{3}{2}$ .

Multiply $- \frac{1}{2} \cdot 0$ .

Multiply $0$ by $- 1$ .

$y = 0 (\frac{1}{2}) + \frac{3}{2}$

Multiply $0$ by $\frac{1}{2}$ .

$y = 0 + \frac{3}{2}$

Add $0$ and $\frac{3}{2}$ .

$y = \frac{3}{2}$

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{3}{2})$

Create a table of the $x$ and $y$ values.

$\begin{array}{c} x & y \\ 0 & \frac{3}{2} \\ 3 & 0 \end{array}$

Step 5

Graph the line using the slope and the y-intercept, or the points.

Slope: $- \frac{1}{2}$

y-intercept: $(0, \frac{3}{2})$

$\begin{array}{c} x & y \\ 0 & \frac{3}{2} \\ 3 & 0 \end{array}$

Step 6

Graph f^-1(x)=-x/2+3/2

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