Let f(x) = 3x2 – x + 2 and g(x) = 5x2 – 1. Find f(g(x)).

- anonymous

Let f(x) = 3x2 – x + 2 and g(x) = 5x2 – 1. Find f(g(x)).

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- anonymous

@johnweldon1993

- anonymous

Will medal AND fan <3

- Nnesha

bec you have to substitute x for x you will get same equation so just
substitute g(x) equation into f(x)

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## More answers

- anonymous

I'm confused

- Astrophysics

\[f(g(x)) = 3(5x^2-1)-(5x^2-1)+2\] notice we take the function g(x) and plug it everywhere there is an x in f(x) which means f(g(x)).

- Astrophysics

\[f(g(x)) = 3(5x^2-1)^2-(5x^2-1)+2\] this is the proper one

- anonymous

Ok. I see

- Astrophysics

Now you may simplify it :)

- anonymous

Can you wait until I finish so you can check my answer? :)

- anonymous

15x^2-3-5x^2+7 yes?

- Astrophysics

Mhm, not quite, notice it's \[3(5x^2-1) \huge ^{2}\]

- anonymous

Ok. I don't understand

- Astrophysics

\[(5x^2-1)^2 \implies (5x^2-1)(5x^2-1)\]

- anonymous

Ohh! Okay

- Astrophysics

Yup :)

- anonymous

25x^4-10x^2+1

- Astrophysics

Awesome, now lets multiply it by 3 \[3(25x^4-10x^2+1)\]

- anonymous

75x^4-30x^2+3

- Astrophysics

That's great :D, now we have \[75x^4-30x^2+3 -(5x^2-1)+2\]

- Astrophysics

Now simplify it a bit more

- anonymous

75x^4-30x^2-5x^2+3

- Astrophysics

Good one more step though, look for like terms

- anonymous

75x^4-35x^2+3

- Astrophysics

Yup, nice work!!

- anonymous

Is that it?

- Astrophysics

Yup, we're done :)

- anonymous

Can I ask one more please? :)

- Astrophysics

\[f(g(x)) = 75x^4-35x^2+3\]

- Astrophysics

Unless you want solutions to it as well, but I doubt it, since it's gross...and sure :)

- anonymous

Lol okay thanks :)

- Astrophysics

And we are solving for x? :)

- anonymous

Solve the equation for the variable. Show each step of your solution process.

- Astrophysics

Sounds fun, any idea how to start

- anonymous

And yes :) You know, the usual

- Astrophysics

See if you can do anything with the 4

- anonymous

subtract it from 5?

- Astrophysics

Yup

- Astrophysics

|dw:1434493963942:dw| so far so good right

- Astrophysics

Now do you know how to deal with the square root

- anonymous

square both sides?

- Astrophysics

Yes! And I'll show you why exactly we do that, so it makes sense...so when we have squareroot anything it means this \[\huge \sqrt{x} \implies x^{1/2}\] and notice if we square it we get 2/2 hence x^1 :), so squaring both sides would be the proper thing to do!

- anonymous

Yay :)

- Astrophysics

Alright so we should have what now?

- anonymous

Add 3 to both sides?

- Astrophysics

|dw:1434494236543:dw|

- anonymous

So, subtract 3 I meant

- Astrophysics

Yes :), and our answer will be? :D

- anonymous

x=-2

- Astrophysics

Yes!! |dw:1434494432642:dw|

- anonymous

HAHAHA :D Yesssss

- anonymous

Ok last one, and I'm done. Pleaseeee

- Astrophysics

Lol ok ok

- anonymous

Given the expression 5a2b – 13ab + 7a3 – 4b, do the following as instructed below:
Write the polynomial in descending order.
Classify the polynomial by the number of terms.
State the degree of the polynomial.

- anonymous

Thank you friend!! *Huge internet hug*

- Astrophysics

Ok lets do it step by step, descending order just means greatest to least (look at the a's).
So go ahead and do that now :)

- anonymous

Isn't it greatest to least?

- Astrophysics

Yes, I made a mistake xD

- Astrophysics

Tried to fix it before you saw haha, but nice catch!

- Astrophysics

Good! Now lets state the terms, and figure out what kind it is!

- anonymous

polynomial?

- Astrophysics

Yes, but I think they might want you to say quadrinomial (meaning 4)

- anonymous

oh okay :)

- anonymous

what about the degree?

- Astrophysics

degree is the highest number of the variables, so we have to sum up the variables for the highest degree, can you figure out which one? :)

- anonymous

3

- Astrophysics

Yup, and that's it!

- anonymous

:( Thank you so much for all your help! You were probably the nicest tutor on here I've met so far!!!

- Astrophysics

Haha, thanks and your welcome :)

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