Question

Given the table below, evaluate the following:

x -3 -2 -1 0 1 2 3 4 5
f(x) 10 20 30 40 50 60 70 80 90
g(x) -1 -2 -3 -4 -5 -6 -7 -8 -9

a. (3f+2g)(1)

b. (f o g)(-1)

Answer 1

hint: (3f+2g)(1) = 3*f(1) + 2*g(1)

Answer 2

So... 3*10*1 + 2*-1*1, 30+(-2)?

Answer 3

what is f(1) equal to?

Answer 4

to find out, locate x = 1 and then look directly below it (to find the f(x) row)

Answer 5

50?

Answer 6

since f(1) = 50, this means 3*f(1) = 3*50

Answer 7

same logic happens with g(1)

Answer 8

So 3*(-5)(1) for g?

Answer 9

g(1) represents the output when you plug in x = 1 into the g(x) function

Answer 10

it's not g times 1

Answer 11

g(1) is all together one number

Answer 12

Oh! So it would just be 3*-5...

Answer 13

2*-5**

Answer 14

My bad.

Answer 15

2*(-5)

Answer 16

so...

(3f+2g)(1) = 3*f(1) + 2*g(1)

(3f+2g)(1) = 3*50 + 2*(-5)

(3f+2g)(1) = ???

Answer 17

150+(-10)
140...

Answer 18

yes

Answer 19

^o^ Awesome! Thank yhu! c:

How would I work B out?

Answer 20

(f o g)(-1) = f( g(-1) )

so you first need to compute g(-1)

that result will be plugged into f(x) to get your final answer

Answer 21

g(-1) = ???

Answer 22

-3

Answer 23

therefore, f( g(-1) ) = f( -3 )

Answer 24

notice how I replaced g(-1) with -3

the two are equal/equivalent so it's valid

Answer 25

now you just need to find f( -3 )

Answer 26

-3*30?

Answer 27

locate -3 on the x row

then look down to the f(x) row

Answer 28

you're thinking that f(-3) is f times -3 which is wrong

Answer 29

Oh! it would be 10

Answer 30

yes, f(-3) is the same as the number 10

Answer 31

input: x = -3

output: f(-3) = 10

rule: unknown function

Answer 32

so that means f( g(-1) ) = 10

and (f o g)(-1) = 10

Answer 33

And that's the answer for B? o.o
Woah... That was actually kind of easy.. n_n

Answer 34

yeah it's not too bad

Answer 35

Thank yhu so much for the help!