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Use Inverse Functions

Use Inverse Functions. Section 6.4. Key Vocabulary. Inverse Function – the original relation and its inverse relation whenever both relations are functions . Inverse Relation – a relation that interchanges the input and output values of the original relation. Inverse Relations in a Table.

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Use Inverse Functions

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  1. Use Inverse Functions Section 6.4

  2. Key Vocabulary • Inverse Function – the original relation and its inverse relation whenever both relations are functions. • Inverse Relation – a relation that interchanges the input and output values of the original relation

  3. Inverse Relations in a Table Original Relation What do you think happens in the inverse relations table? Make a prediction. Inverse Relation Write a sentence that describes what changed. The x and y values switched in the inverse relation.

  4. Example 1: • Step 1: Write the original equation. • Step 2: Switch x and y. • Step 3: Solve for y. • The inverse relation 

  5. Example 2: • Step 1: Show that f(f(x)-1) = x • Step 2: Show that f-1(f(x)) = x

  6. Example 2: • Step 1: Show that f(f(x)-1) = x • Step 2: Show that f-1(f(x)) = x

  7. Example 3: find the inverse of a power function. • Step 1: Write the original equation. • Step 2: Replace f(x) with y. • Step 3: Switch x and y. • Step 4: Solve for y. • The inverse relation 

  8. Class Practice: Take out a sheet of paper.

  9. Class Practice: Take out a sheet of paper.

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