This section provides problems to practice finding the inverse and deciding whether or not the inverse is a function.

Do the problems on your own paper.

  1. The formula for finding the surface area, y, of a cube where x represents the length of one side of the cube. Find the inverse of this formula.
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    y = plus or minus square root of x over 6Close Pop Up
    1. What does the x represent in the inverse?
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      The surface area of the cube. Close Pop Up
    2. What does the y represent in the inverse?
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      The length of one side of the cube.Close Pop Up
    3. Explain in your own words how to find the inverse of a quadratic function.

  2. Select the correct domain and range of the function shown and its inverse.

Limited parabola opens up, vertex (0,-3) & inverse





Domain of f (x):





Range of f (x):



{x | x ≤ – 3}
{x | x ≥ – 3}
{x | x ≤ 0}
{x | x ≥ 0}

{x | x ≤ – 3}
{x | x ≥ – 3}
{x | x ≤ 0}
{x | x ≥ 0}





Domain of f –1 (x):




Range of f –1 (x):



{x | x ≤ – 3}
{x | x ≥ – 3}
{x | x ≤ 0}
{x | x ≥ 0}

{x | x ≤ – 3}
{x | x ≥ – 3}
{x | x ≤ 0}
{x | x ≥ 0}

Domain of f (x)

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{x | x ≥ 0}Close Pop Up

Range of f (x)

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{y | y ≥ – 3}Close Pop Up

Domain of f –1 (x)

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{x | x ≥ – 3}Close Pop Up

Range of f –1 (x)

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{y | y ≥ 0}Close Pop Up

Matching Game

Look at the function in the shaded box. Match the table, the graph, the inverse, and the table and graph of the inverse function by dragging them into the correct table cell.

Interactive exercise. Assistance may be required.

Interactive exercise. Assistance may be required.