Question

How to Define the following functions?

help please..

1. f(x)=x-5; g(x)= x^2-1

a. f+g
b. f-g
c. f⋅g
d. f/g
e. g/f

2. f(x)=√x; g(x)=4-x^2

a. f+g
b. f-g
c. f⋅g
d. f/g
e. g/f

3. f(x)=x^2+1; g(x)=3x-2

a. f+g
b. f-g
c. f⋅g
d. f/g
e. g/f

Answer 1

\[f(x)=x-5;\qquad g(x)=x^2-1\\
\:\\
f+g=f(x)+g(x)=(x-5)+(x^2-1)=\]

Answer 2

??

Answer 3

?? ??

Answer 4

HELP...

Answer 5

f+g is just the sum of f(x) with g(x)

Answer 6

His answer is pretty clear. Read it carefully/slowly.

Answer 7

so (x-5)+(X^2-1) = x^2+x-6

Answer 8

Yep

Answer 9

so thats the answer?? no need to simplify??

Answer 10

B. (x-5)-(X^2-1)= -x^2+x-4

Answer 11

Yep.

Answer 12

C. (x-5) . (X^2-1) = ??? i dont know how to solve if it is a multiplication form..

Answer 13

is it

c. \( f⋅g\)

or

c. \( f\circ g\)

?

Answer 14

also in division form

Answer 15

f times g

Answer 16

c. \( f\times g\)

Answer 17

yeah..

Answer 18

\[ f ×g =(x-5) \times (x^2-1)= (x-5)(x^2-1)=\]

Answer 19

\[\large(\color{orange}a+\color{cornflowerblue}b)(\color{seagreen}c+\color{brown}d)=\color{orange}a\color{seagreen}c+\color{orange}a\color{brown}d+\color{cornflowerblue}b\color{seagreen}c+\color{cornflowerblue}b\color{brown}d\]

Answer 20

\[\large(\overbrace{\overbrace{\color{orange}a
+\underbrace{\color{cornflowerblue}b)(\color{seagreen}c}_{\text{Inside}}}^{\text{First}}
+\color{brown}d}^{\text{Outside}})
=\overbrace{\color{orange}a\color{seagreen}c}^\text F
+\overbrace{\color{orange}a\color{brown}d}^\text O
+\underbrace{\color{cornflowerblue}b\color{seagreen}c}_\text I
+\underbrace{\color{cornflowerblue}b\color{brown}d}_L\\
\large\qquad\quad \underbrace{\qquad\qquad}_{\text{Last}}\]

Answer 21

(x-5)(x^2-1)=(x+x^2)+(x-1)+(-5+x^2)+(-5-1)

Answer 22

@terenzreignz can you help me to answer this??

Answer 23

Please note that these
\[\large(\overbrace{\overbrace{\color{orange}a
+\underbrace{\color{cornflowerblue}b)(\color{seagreen}c}_{\text{Inside}}}^{\text{First}}
+\color{brown}d}^{\text{Outside}})
=\boxed{\overbrace{\color{orange}a\color{seagreen}c}^\text F}
+\boxed{\overbrace{\color{orange}a\color{brown}d}^\text O}
+\boxed{\underbrace{\color{cornflowerblue}b\color{seagreen}c}_\text I}
+\boxed{\underbrace{\color{cornflowerblue}b\color{brown}d}_L}\\
\large\qquad\quad \underbrace{\qquad\qquad}_{\text{Last}}\]

represent MULTIPLICATION not addition...

Answer 24

so they should actually be
(x*x^2)+(x*1)+(-5*x^2)+(-5*-1)

Answer 25

sorry

Answer 26

(x*x^2)+(x*1)+(-5*x^2)+(-5*-1)

Answer 27

good. Now evaluate.

Answer 28

how???? can you guide me,,

Answer 29

What is x times x^2 ?

Answer 30

x^3 ??

Answer 31

Good. So that's the first term
x^3+(x*-1)+(-5*x^2)+(-5*-1)

Answer 32

what's x times -1?

Answer 33

-1x

Answer 34

-5x^2

Answer 35

5

Answer 36

-x suffices.
Can you do the rest? It's just multiplying.

Answer 37

x^3 + -1x + -5x^2 + 5

Answer 38

x^3 - x + (-5*x^2)+(-5*-1)

Answer 39

uhhh
x^3 - x + (-5*x^2)+(-5*-1)

Answer 40

after that whats next??

Answer 41

Just evaluate the multiplications in the parentheses.
Like we did with the x times x^2
and the x times -1.

Answer 42

x^3-x+(-5x^2)+5

Answer 43

What happened?

Answer 44

i dont know...

Answer 45

sorry

Answer 46

Actually, where did the two last terms go?

Answer 47

so where done??

Answer 48

No, that was wrong.... I asked you what happened to the two last terms... (ie why did they disappear?)

Answer 49

IDK

Answer 50

sorry where were we?? im lost

Answer 51

@terenzreignz can we continue plss...

Answer 52

@terenzreignz help please..