Your SlideShare is downloading. ×
4 5 inverse functions
Upcoming SlideShare
Loading in...5
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Text the download link to your phone
Standard text messaging rates apply

4 5 inverse functions

318

Published on

Published in: Education, Technology
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
318
On Slideshare
0
From Embeds
0
Number of Embeds
4
Actions
Shares
0
Downloads
16
Comments
0
Likes
0
Embeds 0
No embeds

Report content
Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
No notes for slide

Transcript

  • 1. 4-5 INVERSE FUNCTIONS Objectives: 1. Find the inverse of a function, if it exists.
  • 2. INVERSE EXAMPLE Conversion formulas come in pairs, for example: These formulas “undo” each other, so they are inverses.
  • 3. DEFINITION OF INVERSES Two functions f and g are inverses if: f(g(x)) = x and g(f(x)) = x To check if two functions are inverses, perform both compositions and make sure both equal x.
  • 4. EXAMPLE 1 If and show that f and g are inverses.
  • 5. YOU TRY! Show that are inverses. and
  • 6. INVERSE NOTATION The inverse of f is written f -1 f -1(x) Note: is the value of f -1 at x is not
  • 7. FINDING INVERSES graph of f -1 is the reflection of f over the line y = x Can be found by switching x and y in the ordered pairs. Find equation of f -1 by switching x and y in the equation and solving for y. The
  • 8. EXAMPLE 2 f(x) = 4 – x2 for x 0. Sketch the graph of f and f -1 (x) Find a rule for f -1 (x) Let
  • 9. YOU TRY! g(x) = (x – 4)2 – 1 for x 4. Sketch the graph of g and g -1 (x) Find a rule for g -1 (x) Let
  • 10. EXAMPLE 3 Suppose a function f has an inverse. If f(2) = 3, find: f -1 (3) f(f -1(3)) f -1(f(2))
  • 11. YOU TRY! Suppose a function g has an inverse. If g(5) = 1, find: g -1 (1) g -1(g(5)) g(g -1(1))
  • 12. DO ALL FUNCTIONS HAVE INVERSES? the graph of y = x2 over the line y = x. Is the result a function? Reflect
  • 13. ONE-TO-ONE Only functions that are one-to-one have inverses. One-to-one means each x value has exactly one y value and each y has exactly one x Can check using horizontal line test.
  • 14. EXAMPLE 4 Which functions are one-to-one? Which have inverses?
  • 15. YOU TRY! Is h(x) one-to-one?  Does it have an inverse? 
  • 16. EXAMPLE 5 State whether each function has an inverse. If yes, find f -1 (x) and show f(f -1(x)) = f -1(f(x)) = x  
  • 17. YOU TRY! Does have an inverse? If so, find f -1 (x).

×