Question

if f(x)=x^2-3x and g(x)=√x-1 then f(g(x))

Answer 1

You'd have\[(\sqrt{x}-1)^{2}-3x\]I'm not sure it's its sqrt x or sqrt x-1, so you may have to change that.

Answer 2

f(x)=x^2-3x and g(x)=√x-1

so,

f(g(x)) = ((x-1)^(1/2))^2 - 3(x-1)^(1/2)

or

\[f(g(x)) = (\sqrt{x-1})^2 - 3\sqrt{x-1}\]

Answer 3

why did you ask the same question over again?

Answer 4

what comes after that?

Answer 5

remember,

Rules:

\[\sqrt{x} =x^{\frac{1}{2}}\]

\[x^{a}x^{b} = x^{a + b}\]

Answer 6

for example,

\[x^{2}x^{3} = x^{2+3} = x^{5}\]

Also note that,

\[x^{1} = x\]

And just so you understand

\[x^2 = x*x\]
\[x^3 = x*x*x\]

etc.

Answer 7

oh i forgot about that, but i have remenber now, but i still get the worng answer

Answer 8

so first write this as it is its expanded form based on the definition of an exponent (last rule I showed you)
\[(\sqrt{x-1})^2 = ((x-1)^{\frac{1}{2}})^2\]

Answer 9

they expect simplification right?

Answer 10

I hope you understand what I mean? If not I can just write it out for you

Answer 11

please

Answer 12

Fine fine,

\[((x-1)^{\frac{1}{2}})^2 = (x-1)^{\frac{1}{2}}*(x-1)^{\frac{1}{2}}\]

Answer 13

do you see what I'm doing? and how to simplify this?

Answer 14

all the rules I gave you apply to your problem

Answer 15

wait is √x then -1

Answer 16

is not together

Answer 17

is it?
\[\sqrt{x} - 1\]
or is it?
\[\sqrt{x - 1}\]

Answer 18

sorry but in my defence it was ambiguous, next time make sure you use brackets

Answer 19

the first one, sorry

Answer 20

so can you write the expression out? I can go over the simplification with you

Answer 21

you know what f(g(x)) is right?

Answer 22

you just replace x with (x)^(1/2) - 1 in f(x)

Answer 23

yes i know all of that ill write it out over again

Answer 24

if f(x)=x^2-3x and g(x)=√x -1 then f(g(x))

Answer 25

so,

\[(x^\frac{1}{2} - 1)^2 - 3(x^\frac{1}{2} - 1)\]

Answer 26

ok

Answer 27

they want you to simplify it right?

Answer 28

so first expand the exponent on the first term in f(g(x)) like I did previously

Answer 29

the answer is x-5√x +4 , but i dont know how to get there

Answer 30

They want you to simplify it so first expand the exponent in f(g(x))

Answer 31

remember the rule,

x^2 = x*x
x^3 = x*x*x
etc...

similarly

(x+1)^2 = (x+1)(x+1)
(x+1)^3 = (x+1)(x+1)(x+1)
etc...

Answer 32

so first off you want to expand all your whole number exponents

Answer 33

look back to when I thought g(x) = (x -1)^(1/2)

Answer 34

can you do it please, im getting confused

Answer 35

I'm not here to do your work for you, I will only guide you. Math is confusing but just be patient and you will understand it.

sorry im not being clear I will try to be more clear from here on out.

first step expand this term in the equation ((x)^(1/2) - 1)^2

this is an example of an expansion:
(x+1)^3 = (x+1)(x+1)(x+1)

Answer 36

I want you to learn this stuff and understand it so you dont struggle with it because it isnt going away. Algebra is actually very simple once you understand the rules

Answer 37

can you show me the first step?

Answer 38

\[((x)^{\frac{1}{2}} - 1)^2 = ?\]

just expand this that is your first step

Answer 39

i know math is just this equation that i dont remenber, i dont have your time, i skiped this one to do the rest of my equations

Answer 40

algebra is just a few simple rules, just please try expanding the term I showed you I will help you with the next step if you do, just make a guess

Answer 41

nevermine ,

Answer 42

there is no shame in being wrong, please dont give up

Answer 43

If you get it wrong I will give you the right answer

Answer 44

Just work with me try to apply the rules I show you

Answer 45

hey im not giving up i already got it when you told me the about the square root than converts to on half , you make this too long

Answer 46

dont anwer

Answer 47

Im not making this long I'm only asking you to go through the simplification step by step or you could show me your work

Answer 48

instead you just argue with me.

Answer 49

what ever I dont have time for this here is the answer

Answer 50

First step expand:
\[(x^{\frac{1}{2}} -1)^2 -3(x^{\frac{1}{2}} - 1) = (x^{\frac{1}{2}} - 1)(x^{\frac{1}{2}} - 1) - 3(x^{\frac{1}{2}} - 1) \]

Second step you distribute (a + b)(d + c) = ad + ac + bd + bc
\[(x^{\frac{1}{2}} - 1)(x^{\frac{1}{2}} - 1) - 3(x^{\frac{1}{2}} - 1) = x^{\frac{1}{2}}x^{\frac{1}{2}} - x^{\frac{1}{2}} - x^{\frac{1}{2}} + (-1)(-1) - 3(x^{\frac{1}{2}} - 1)\]

Third step distribute the 3 so b(a+c) = ba + bc
\[x^{\frac{1}{2}}x^{\frac{1}{2}} - x^{\frac{1}{2}} - x^{\frac{1}{2}} + 1 + (- 3)x^{\frac{1}{2}} + (- 1)(-3)\]

forth step collect terms also add exppnents
\[x^{\frac{1}{2}}x^{\frac{1}{2}} - x^{\frac{1}{2}} - x^{\frac{1}{2}} + 1 - 3x^{\frac{1}{2}} + 3 = x^{\frac{1}{2} + \frac{1}{2}} - 2x^{\frac{1}{2}} - 3x^{\frac{1}{2}} + 4\]

\[x^{1} - 5x^{\frac{1}{2}} + 4 = x- 5x^{\frac{1}{2}} + 4\]

Answer 51

Hope this helps probably how I should have went about it in the first place

Answer 52

You probably wont even seen it but whatevers