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

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

Mathematics
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Will medal AND fan <3
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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I'm confused
\[f(g(x)) = 3(5x^2-1)-(5x^2-1)+2\] notice we take the function g(x) and plug it everywhere there is an x in f(x) which means f(g(x)).
\[f(g(x)) = 3(5x^2-1)^2-(5x^2-1)+2\] this is the proper one
Ok. I see
Now you may simplify it :)
Can you wait until I finish so you can check my answer? :)
15x^2-3-5x^2+7 yes?
Mhm, not quite, notice it's \[3(5x^2-1) \huge ^{2}\]
Ok. I don't understand
\[(5x^2-1)^2 \implies (5x^2-1)(5x^2-1)\]
Ohh! Okay
Yup :)
25x^4-10x^2+1
Awesome, now lets multiply it by 3 \[3(25x^4-10x^2+1)\]
75x^4-30x^2+3
That's great :D, now we have \[75x^4-30x^2+3 -(5x^2-1)+2\]
Now simplify it a bit more
75x^4-30x^2-5x^2+3
Good one more step though, look for like terms
75x^4-35x^2+3
Yup, nice work!!
Is that it?
Yup, we're done :)
Can I ask one more please? :)
\[f(g(x)) = 75x^4-35x^2+3\]
Unless you want solutions to it as well, but I doubt it, since it's gross...and sure :)
Lol okay thanks :)
And we are solving for x? :)
Solve the equation for the variable. Show each step of your solution process.
Sounds fun, any idea how to start
And yes :) You know, the usual
See if you can do anything with the 4
subtract it from 5?
Yup
|dw:1434493963942:dw| so far so good right
Now do you know how to deal with the square root
square both sides?
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!
Yay :)
Alright so we should have what now?
Add 3 to both sides?
|dw:1434494236543:dw|
So, subtract 3 I meant
Yes :), and our answer will be? :D
x=-2
Yes!! |dw:1434494432642:dw|
HAHAHA :D Yesssss
Ok last one, and I'm done. Pleaseeee
Lol ok ok
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.
Thank you friend!! *Huge internet hug*
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 :)
Isn't it greatest to least?
Yes, I made a mistake xD
Tried to fix it before you saw haha, but nice catch!
Good! Now lets state the terms, and figure out what kind it is!
polynomial?
Yes, but I think they might want you to say quadrinomial (meaning 4)
oh okay :)
what about the degree?
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? :)
3
Yup, and that's it!
:( Thank you so much for all your help! You were probably the nicest tutor on here I've met so far!!!
Haha, thanks and your welcome :)

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