1 / 13

Inverse Functions

Inverse Functions. Review from Math I. Relation – a mapping of input values (x-values) onto output values (y-values). Here are 3 ways to show the same relation. x y -2 4 -1 1 0 0 1 1. y = x 2. Equation Table of values Graph. x y -2 -1 0 0

stansburyd
Download Presentation

Inverse Functions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Inverse Functions

  2. Review from Math I • Relation – a mapping of input values (x-values) onto output values (y-values). • Here are 3 ways to show the same relation. x y -2 4 -1 1 0 0 1 1 y = x2 Equation Table of values Graph

  3. x y • -2 • -1 • 0 0 • 1 1 x = y2 • Inverse relation – just think: switch the x & y-values. ** the inverse of an equation: switch the x & y and solve for y. ** the inverse of a table: switch the x & y. ** the inverse of a graph: the reflection of the original graph in the line y = x.

  4. Ex: Find an inverse of y = -3x+6. • Steps: -switch x & y -solve for y y = -3x+6 x = -3y+6 x-6 = -3y

  5. 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. Symbols: f -1(x) means “f inverse of x”

  6. Ex: Verify that f(x)=-3x+6 and g(x)=-1/3x+2 are inverses. • Meaning find f(g(x)) and g(f(x)). If they both equal x, then they are inverses. f(g(x))= -3(-1/3x+2)+6 = x-6+6 = x g(f(x))= -1/3(-3x+6)+2 = x-2+2 = x ** Because f(g(x))=x and g(f(x))=x, they are inverses.

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

  8. Ex: (a)Find the inverse of f(x)=x5. (b) Is f -1(x) a function? (hint: look at the graph! Does it pass the vertical line test?) • y = x5 • x = y5 Yes , f -1(x) is a function.

  9. Horizontal Line Test • Used to determine whether a function’s inverse will be a function by seeing if the original function passes the horizontal line test. • If the original function passes the horizontal line test, then its inverse is a function. • If the original function does not pass the horizontal line test, then its inverse is not a function.

  10. Ex: Graph the function f(x)=x2 and determine whether its inverse is a function. Graph does not pass the horizontal line test, therefore the inverse is not a function.

  11. Ex: f(x)=2x2-4 Determine whether f -1(x) is a function, then find the inverse equation. y = 2x2-4 x = 2y2-4 x+4 = 2y2 OR, if you fix the tent in the basement… f -1(x) is not a function.

  12. Ex: g(x)=2x3 y=2x3 x=2y3 OR, if you fix the tent in the basement… Inverse is a function!

  13. Assignment#1-16 EVENS ONLY, show work for all & check answers at the of the link:http://cdn.kutasoftware.com/Worksheets/Alg2/Function%20Inverses.pdf

More Related