Question

PLEASE HELP!!!

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

Answer 1

@ganeshie8 @robtobey

Answer 2

is it 5x^2-1 or 5x=2-1?

Answer 3

5x+2-1

Answer 4

sorry it's g(x) = 5x^2 - 1

Answer 5

oh okay

Answer 6

are you looking for where they intersect

Answer 7

?

Answer 8

no I'm looking for f(g(x))

Answer 9

whats F(g(x))?

Answer 10

I'm not sure, which is why I need help

Answer 11

oh

Answer 12

take your function, \(f(\color{red}{x}) = 3\color{red}{x^2}-\color{red}{x}+2\) and replace every red colored x with \(\color{red}{5x^2-1}\)

Answer 13

Simplify that and you will have \(f(g(x))\)

Answer 14

okay, let me work this out

Answer 15

There was a typo, haha. \[f(g(x)) = 3(5x^2-1)^2 -(5x^2-1) +2\]

Answer 16

Refer to the attachment from the Mathematica program.

Answer 17

okay, I think I worked it out. is the answer f(g(x)) = 25x^4 - 6 ?!?!

Answer 18

\[f(g(x)) = 3( 24x^4-10x^2+1) -5x^2+1+2\]\[f(g(x)) = 72x^4 -30x^2+3-5x^2+3\]\[f(g(x))= 72x^4-(30+5)x^2+6\]\[\boxed{\color{red}{f(g(x)) = 72x^4 -35x^2+6}}\]

Answer 19

I think you made a mistake expanding \((5x^2-1)^2\)

Answer 20

wait, how did you get from f(g(x))=3(5x^2−1)^2−(5x^2−1)+2 to f(g(x))=3(24x^4−10x^2+1)−5x^2+1+2

Answer 21

@Jhannybean ?!

Answer 22

I expanded \((5x^2-1)^2\)

Think of \(a=5x^2\) and \(b=1\). Now do you recall the form \(ax^2-2ab+b^2\)? This is the expansion of a polynomial in the form \((a-b)^2\)

Answer 23

Are you with me so far?

Answer 24

oh. but then shouldn't it be f(g(x)) = 75x^4 - 30x^2 + 3 − 5x^2 + 1 + 2 instead of having 72x^4?

Answer 25

f(g(x)) = 3(5x^2 - 1)^2 - (5x^2 - 1) + 2
f(g(x)) = 3(25x^4 - 10x^2 + 1) - (5x^2 - 1) + 2
f(g(x)) = 75x^4 - 30x^2 + 3 - 5x^2 + 1 + 2
f(g(x)) = 72x^4 - 35x^2 + 6

Answer 26

Oh yes it was my fault. I found it. I wrote 24 instead of 25. You are right. It should be 75 ^^

Answer 27

\[f(g(x)) = 3( \color{blue}{24x^4}-10x^2+1) -5x^2+1+2\] SO when I was solving it I got 72x\(^4\) instead of 75x\(^4\)

Answer 28

oh, so the answer is f(g(x)) = 75x^4 - 35x^2 + 6?

Answer 29

Yep.

Answer 30

thanks :)

Answer 31

Good job on spotting that error.

Answer 32

lol thanks