Question

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

Answer 1

@johnweldon1993

Answer 2

Will medal AND fan <3

Answer 3

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

Answer 4

I'm confused

Answer 5

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

Answer 6

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

Answer 7

Ok. I see

Answer 8

Now you may simplify it :)

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

Ok. I don't understand

Answer 13

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

Answer 14

Ohh! Okay

Answer 15

Yup :)

Answer 16

25x^4-10x^2+1

Answer 17

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

Answer 18

75x^4-30x^2+3

Answer 19

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

Answer 20

Now simplify it a bit more

Answer 21

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

Answer 22

Good one more step though, look for like terms

Answer 23

75x^4-35x^2+3

Answer 24

Yup, nice work!!

Answer 25

Is that it?

Answer 26

Yup, we're done :)

Answer 27

Can I ask one more please? :)

Answer 28

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

Answer 29

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

Answer 30

Lol okay thanks :)

Answer 31

And we are solving for x? :)

Answer 32

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

Answer 33

Sounds fun, any idea how to start

Answer 34

And yes :) You know, the usual

Answer 35

See if you can do anything with the 4

Answer 36

subtract it from 5?

Answer 37

Yup

Answer 38

so far so good right