Mehlala ea Lipotso Tse Buisanang ka ho Eketsa le ho Tlosa Mesebetsi
Ho eketsa le ho tlosa mesebetsi ke mohopolo oa motheo le oa bohlokoa lipalo. Khopolo ena ha e bohlokoa feela maemong a thuto empa hape e na le lits'ebetso tse ngata tse sebetsang bophelong ba letsatsi le letsatsi le mafapheng a mang a thuto. Sehloohong sena, re tla tšohla mehlala e 'maloa ea mathata a ho eketsa le ho tlosa, hammoho le litlhaloso tse qaqileng.
Litlhaloso tsa Motheo le Mehopolo
Pele re kena lipotsong tsa mohlala, ha re buisaneng hanyane ka tlhaloso le mehopolo ea motheo ea mesebetsi ea ho eketsa le ho ntša.
Ho eketsa mesebetsi
Haeba re na le mesebetsi e 'meli \( f(x) \) le \( g(x) \), joale kakaretso ea mesebetsi ena e 'meli ke mosebetsi o mocha o hlalosoang e le:
\[ (f + g)(x) = f(x) + g(x) \]
Phokotso ea Mesebetsi
Ho ntsha mesebetsi le hona ho hlaloswa ka tsela e tshwanang le ho eketsa mesebetsi. Haeba re na le mesebetsi e mmedi \( f(x) \) le \( g(x) \), ho ntsha mesebetsi ena e mmedi ke mosebetsi o motjha o hlaloswang e le:
\[ (f – g)(x) = f(x) – g(x) \]
Lipotso tsa Mehlala le Puisano
A re shebeng mehlala e meng ea mathata ho hlakisa mohopolo ona.
Mohlala oa 1: Ho Eketsoa ha Mesebetsi e Methati
A re re \( f(x) = 2x + 3 \) le \( g(x) = x – 1 \). Fumana \( (f + g)(x) \).
Puisano:
Re ka eketsa mesebetsi ena e 'meli ka ho eketsa mantsoe a tsamaellanang.
\[
(f + g)(x) = f(x) + g(x)
\]
\[
(f + g)(x) = (2x + 3) + (x – 1)
\]
\[
(f + g)(x) = 2x + x + 3 – 1
\]
\[
(f + g)(x) = 3x + 2
\]
Kahoo, \( (f + g)(x) = 3x + 2 \).
Mohlala oa 2: Ho tlosa Mesebetsi e Methati
A re re \( f(x) = 4x + 5 \) le \( g(x) = 2x – 3 \). Fumana \( (f – g)(x) \).
Puisano:
Re ka fokotsa mesebetsi ka bobeli ka ho tlosa mantsoe a tsamaellanang.
\[
(f – g)(x) = f(x) – g(x)
\]
\[
(f – g)(x) = (4x + 5) – (2x – 3)
\]
\[
(f – g)(x) = 4x + 5 – 2x + 3
\]
\[
(f – g)(x) = 2x + 8
\]
Kahoo, \( (f – g)(x) = 2x + 8 \).
Mohlala oa 3: Ho eketsoa ha Mesebetsi ea Quadratic
A re re \( f(x) = x^2 + 2x + 1 \) le \( g(x) = -x^2 + 4x – 3 \). Fumana \( (f + g)(x) \).
Puisano:
Re ka eketsa mesebetsi ena e 'meli ka ho eketsa mantsoe a tsamaellanang.
\[
(f + g)(x) = f(x) + g(x)
\]
\[
(f + g)(x) = (x^2 + 2x + 1) + (-x^2 + 4x – 3)
\]
\[
(f + g)(x) = x^2 – x^2 + 2x + 4x + 1 – 3
\]
\[
(f + g)(x) = 6x – 2
\]
Kahoo, \( (f + g)(x) = 6x – 2 \).
Mohlala oa 4: Ho Tlosa Mesebetsi ea Quadratic
A re re \( f(x) = 3x^2 – 2x + 4 \) le \( g(x) = x^2 + x – 5 \). Fumana \( (f – g)(x) \).
Puisano:
Re ka fokotsa mesebetsi ka bobeli ka ho tlosa mantsoe a tsamaellanang.
\[
(f – g)(x) = f(x) – g(x)
\]
\[
(f – g)(x) = (3x^2 – 2x + 4) – (x^2 + x – 5)
\]
\[
(f – g)(x) = 3x^2 – x^2 – 2x – x + 4 + 5
\]
\[
(f – g)(x) = 2x^2 – 3x + 9
\]
Kahoo, \( (f – g)(x) = 2x^2 – 3x + 9 \).
Mohlala oa 5: Ho eketsa le ho tlosa mesebetsi ea Exponential
A re re \( f(x) = e^x \) le \( g(x) = e^{-x} \). Fumana:
1. \( (f + g)(x) \)
2. \( (f – g)(x) \)
Puisano:
1. Mosebetsi oa ho Eketsa:
\[
(f + g)(x) = f(x) + g(x)
\]
\[
(f + g)(x) = e^x + e^{-x}
\]
Kahoo, \( (f + g)(x) = e^x + e^{-x} \).
2. Phokotso ea Mesebetsi:
\[
(f – g)(x) = f(x) – g(x)
\]
\[
(f – g)(x) = e^x – e^{-x}
\]
Kahoo, \( (f – g)(x) = e^x – e^{-x} \).
Mohlala oa 6: Ho eketsa le ho tlosa mesebetsi ea Trigonometric
A re re \( f(x) = \sin x \) le \( g(x) = \cos x \). Fumana:
1. \( (f + g)(x) \)
2. \( (f – g)(x) \)
Puisano:
1. Mosebetsi oa ho Eketsa:
\[
(f + g)(x) = f(x) + g(x)
\]
\[
(f + g)(x) = \sin x + \cos x
\]
Kahoo, \( (f + g)(x) = \sin x + \cos x \).
2. Phokotso ea Mesebetsi:
\[
(f – g)(x) = f(x) – g(x)
\]
\[
(f – g)(x) = \sin x – \cos x
\]
Kahoo, \( (f – g)(x) = \sin x – \cos x \).
Mohlala oa 7: Tšebeliso ea ho Eketsa le ho Tlosa Mesebetsi Mathata a 'Mele
A re re ho na le mesebetsi e 'meli e hlalosang boemo (ka limithara) ba likoloi tse peli tse tsamaeang tseleng e tšoanang ka nako \( t \) (ka metsotsoana).
Koloi A: \( f(t) = 5t + 2 \)
Koloi B: \( g(t) = 3t + 4 \)
Etsa qeto:
1. Sebaka se kopaneng sa likoloi tse peli.
2. Phapang boemong ba likoloi tse peli ka nako \(t \).
Puisano:
1. Mosebetsi oa ho Eketsa:
\[
(f + g)(t) = f(t) + g(t)
\]
\[
(f + g)(t) = (5t + 2) + (3t + 4)
\]
\[
(f + g)(t) = 8t + 6
\]
Kahoo, boemo bo kopaneng ba likoloi tse peli ka nako \(t \) ke \(8t + 6 \) limithara.
2. Phokotso ea Mesebetsi:
\[
(f – g)(t) = f(t) – g(t)
\]
\[
(f – g)(t) = (5t + 2) – (3t + 4)
\]
\[
(f – g)(t) = 2t – 2
\]
Kahoo, phapang boemong ba likoloi tse peli ka nako ke limithara tse 2t – 2.
Qetello
Ho eketsa le ho tlosa mesebetsi ke mehopolo ea bohlokoa haholo ea motheo lipalo. Re ka eketsa kapa ra ntša mesebetsi e 'meli ka ho eketsa kapa ho tlosa mantsoe a tsamaellanang. Khopolo ena ha e na thuso feela maemong a thuto, empa hape e na le lits'ebetso tse ngata tse sebetsang. Ka mehlala e fapaneng ea lipotso tse kaholimo, ho tšeptjoa hore babali ba ka utloisisa khopolo ena hamolemo.
