Question

Please help with this pre-cal
questions in the attachment.

Answer 1

do u know the meaning of using [ ] or () brackets ?

Answer 2

Yes

Answer 3

well ... then ur 1st Question ask for a function ( which i will denote by f(x) ) which should be greater than or equal to 0 but lesser than + infinity ..... usually functions with square roots belongs to this type

Answer 4

\[f(x) = \sqrt{x}\] this is a very simple example

Answer 5

u cant find the square root of \[\sqrt{-3}\] or any other negative number.... got it ?

Answer 6

Okay, got it.

Answer 7

the second one says... a function which is greater than - infinity and lesser than + infinity... usually ...almost any linear function satisfy this

Answer 8

\[f(x) = x + 8 \]\[f(x) = 5x + 10 \]....like any u like...

Answer 9

Oh okay

Answer 10

these functions can take either negative or positive values... no harm happens :)

Answer 11

Okay cool

Answer 12

now for the last one... its the same as the second one ..but it cant be equal to zero...usually a function with this range means that the function is a fraction ...like the below one

Answer 13

\[f(x) = \frac{ 5x + 8 }{ x}\]

Answer 14

if u substitute 0 in the above one...u wont be able to tell what will be the answer... because a number divide by zero could be either + infinity or - infinity

Answer 15

Right, ok, got it.

Answer 16

:)

Answer 17

soo... in a fraction the denominator cant be zero... any function with a fraction where the denominator will be 0 when x is 0 will be ur answer for the third and last of ur first question :)

Answer 18

now... do u want help in the 2nd one too ?

Answer 19

Yes please. Thank you for helping me with the first question! :)

Answer 20

u r welcome :) lets c... the 2nd one

Answer 21

they say the original price is "x"
and the price after you apply the coupon is f(x) ......

what happens when u applied the coupon is.... the cut off 25 dollars .....

so if the price of ur dress is "x" ...after u apply the coupon ..the price is " x -25 " ...because they cut off 25$

Answer 22

so... f(X) = X -25 ...got it ?

Answer 23

Okay I understand that

Answer 24

now lets consider g(x) .....
g(x) is the price of dress withe the 20% discount applied....
a 20% discount means that u can buy the dress less than 20% of the original price

if the original price is "x"

then 20% of "x" is (20/100)x

then g(x) = x - (20/100)x got it ?

Answer 25

Yes that makes sense

Answer 26

and finally ....
( f o g )(x) means f( g (x) )...where u have to substituent g(x) instead of "x" in f(x)

therefor
(f o g)(x) = g(x) - 25
= x - (20/100)x - 25

Answer 27

in the same way (g o f)(x) means g ( f(x) ) where u have to substitute "f(x)" instead of "x" in "g(x)"
therefor
(g o f)(x) = f(x) - (20/100)f(x)
= x - 25 - [ (20/100)( x -25) ]

Answer 28

i hope u understand it :)

Answer 29

Those two I was really confused on, but I understand them now :)

Answer 30

Thank you sooo much!! I really appreciate it! :)

Answer 31

u r welcome :)