Finding Inverses thru algebra Proving Inverses thru composition

Finding Inverses (thru algebra) & Proving Inverses (thru composition) MM 2 A 5 b. Determine inverses of linear, quadratic, and power functions and functions of the form f(x) = xa, including the use of restricted domains. MM 2 A 5 d. Use composition to verify that functions are inverses of each other.

Finding Inverses of Functions using ALGEBRA!!

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

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

Example 2: Find the inverse of f(x) = x 2 - 5. Ø Steps: -change f(x) to y -switch x & y -solve for y

Example 3: Find the inverse of f(x) = x 3 - 4. Ø Steps: -change f(x) to y -switch x & y -solve for y

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

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

You Try!! 2) Find the inverse of f(x) = 2 x 2 - 6.

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

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

Proving Functions are Inverses using COMPOSITION!!

Inverse Functions Ø 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: f -1(x) means “f inverse of x”

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

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

You Try!! 2) Verify that f(x) = and g(x) = x 2 - 4 are inverses.

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