Finding Inverses (thru algebra) & Proving Inverses (thru composition) MM2A5b. Determine inverses of linear, quadratic, and power functions and functions.

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Finding Inverses (thru algebra) & Proving Inverses (thru composition) MM2A5b. Determine inverses of linear, quadratic, and power functions and functions of the form f(x) = x a, including the use of restricted domains. MM2A5d. Use composition to verify that functions are inverses of each other.

Finding Inverses of Functions usingALGEBRA!!

To find the inverse of a function: 1. Change the f(x) to a y. 2. Switch the x & y values. 3. Solve the new equation for y. ** Remember functions have to pass the vertical line test!

Example 1: Find the inverse of f(x) = -3x + 6.  Steps: -change f(x) to y -switch x & y -solve for y -solve for y

Example 2: Find the inverse of f(x) = x  Steps: -change f(x) to y -switch x & y -solve for y -solve for y

Example 3: Find the inverse of f(x) = x  Steps: -change f(x) to y -switch x & y -solve for y -solve for y

Example 4: Find the inverse of f(x) =.  Steps: -change f(x) to y -switch x & y -solve for y -solve for y

You Try!! 1) Find the inverse of f(x) = 2x - 1.

You Try!! 2) Find the inverse of f(x) = 2x

You Try!! 3) Find the inverse of f(x) =.

You Try!! 4) Find the inverse of f(x) =.

Proving Functions are Inverses usingCOMPOSITION!!

Inverse Functions  Given 2 functions, f(x) & g(x), if f(g(x)) = x AND g(f(x)) = x, then f(x) & g(x) are inverses of each other. Remember: Remember: f -1 (x) means “f inverse of x”

Example 1: Verify that f(x) = -3x+6 and g(x) = -1 / 3 x+2 are inverses.  Steps:- Find f(g(x)) and g(f(x)). - If they both equal x, then they are inverses.

Example 2: Verify that f(x) = x and g(x) = are inverses.  Steps:- Find f(g(x)) and g(f(x)). - If they both equal x, then they are inverses.

You Try!! 1) Verify that f(x) = 3x - 4 and g(x) = are inverses.

You Try!! 2) Verify that f(x) = and g(x) = x are inverses.

You Try!! 4) Verify that f(x) = and g(x) = are inverses.