Inverse Functions
Gbogbo ọrọ náà
You already know how a function turns an input into an output. An inverse function does the reverse: it takes the output back to the input it came from. Think of it as the undo button for a function. If one machine doubles a number and adds three, the inverse machine must subtract three and then halve, exactly reversing each step in the opposite order.
But not every function can be undone. In this lesson you will learn the crucial test of whether an inverse even exists, why a function must be one-one to have one, and the reliable swap-and-rearrange method for finding the inverse. These ideas sit at the heart of the Functions section and reward careful, tidy algebra.
Ebumnobi
- Explain in words why a given function does not have an inverse.
- Find the inverse of a one-one function and use correct notation.
Akọmọ Ojú-ẹkọ
Ọ dị na ngwa Green Bridge
Budata ngwa Green Bridge CBT na ekwentị maọbụ kọmputa gị iji nweta akwụkwọ ndụmọdụ zuru oke, ajụjụ mmụta, na ndị ọzọ.
Ayẹwo Ẹkọ
Ekele diri gi maka imecha ihe karịrị na Inverse Functions. Ugbu a na ị na-enyochakwa isi echiche na echiche ndị dị mkpa, ọ bụ oge iji nwalee ihe ị ma. Ngwa a na-enye ụdị ajụjụ ọmụmụ dị iche iche emebere iji kwado nghọta gị wee nyere gị aka ịmata otú ị ghọtara ihe ndị a kụziri.
Ị ga-ahụ ngwakọta nke ụdị ajụjụ dị iche iche, gụnyere ajụjụ chọrọ ịhọrọ otu n’ime ọtụtụ azịza, ajụjụ chọrọ mkpirisi azịza, na ajụjụ ede ede. A na-arụpụta ajụjụ ọ bụla nke ọma iji nwalee akụkụ dị iche iche nke ihe ọmụma gị na nkà nke ịtụgharị uche.
Jiri akụkụ a nke nyocha ka ohere iji kụziere ihe ị matara banyere isiokwu ahụ ma chọpụta ebe ọ bụla ị nwere ike ịchọ ọmụmụ ihe ọzọ. Ekwela ka nsogbu ọ bụla ị na-eche ihu mee ka ị daa mba; kama, lee ha anya dị ka ohere maka ịzụlite onwe gị na imeziwanye.
- What is the inverse of f(x) = 2x + 3? A. (x - 3)/2 B. (x + 3)/2 C. 2x - 3 D. 1/(2x + 3) Answer: A
- Which type of function always has an inverse? A. Many-one B. One-one C. Quadratic over all reals D. Constant Answer: B
- Why does g(x) = x^2 (for all real x) have no inverse? A. It is undefined at 0 B. It is one-one C. It is many-one, since 2 and -2 both give 4 D. It has no range Answer: C
- The inverse of f(x) = x/4 - 5 is: A. 4x - 5 B. 4(x + 5) C. (x - 5)/4 D. 1/(x/4 - 5) Answer: B
- If f(4) = 11, what is f^{-1}(11)? A. 11 B. 1/11 C. 4 D. 7 Answer: C
Ọ dị na ngwa Green Bridge
Budata ngwa Green Bridge CBT na ekwentị maọbụ kọmputa gị iji nweta akwụkwọ ndụmọdụ zuru oke, ajụjụ mmụta, na ndị ọzọ.
Ọ dị na ngwa Green Bridge
Budata ngwa Green Bridge CBT na ekwentị maọbụ kọmputa gị iji nweta akwụkwọ ndụmọdụ zuru oke, ajụjụ mmụta, na ndị ọzọ.
Àwọn Ìwé Tó Dáa Láti Kà
Meecha Ajụjụ Ule Ọmarịcha
Ị chọrọ ime ajụjụ ule ọmarịcha gbasara Inverse Functions? Budata ngwa Green Bridge CBT iji nweta ajụjụ ule ọmarịcha na nyocha zuru ezu gbasara isiokwu a.
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