Question

Need help with a discrete math problem.

Answer 1

Have you solved any of them? Do you know how to take the composite of two functions?

Answer 2

I am thinking f of g would be would be like f(g(x))

Answer 3

so for (a) we must be looking at f(f(x)) if that is right

Answer 4

But I don't understand the mapping R into R part

Answer 5

Mapping from R to R just means that its domain is a subset of the real numbers and its range is a subset of the real numbers

Answer 6

ah, that makes sense.

Answer 7

What about writing k(x) in terms of x

Answer 8

Would that just be for (a) k(x) = (x^2)^2

Answer 9

It just means that you should have k equal something involving only x's. Yeah, that's right.

Answer 10

ok cool I'm sure I can figure out the rest then. Thanks for the help! :)

Answer 11

b. k(x) = g(g(x)) = root((root(x^2)+1)^2 + 1)

Answer 12

Yup, and that simplifies to \(\sqrt{x^2+2}\).

Answer 13

ah ok, awesome

Answer 14

c. k(x) = h(g(x)) = 3(root(x^2+1))

Answer 15

d. k(x) = g(h(x) = root((3x - 1)^2 + 1)

Answer 16

e. k(x) = f(g(h(x))) = (root((3x - 1)^2 + 1))^2

Answer 17

They are all correct except c. And e can be simplified.

Answer 18

c. 3root(x^2+1)

Answer 19

You are still missing the -1 at the end ;)

Answer 20

\(h(x)=3x-1\)

Answer 21

3(root(x^2+1) - 1)

Answer 22

ah I see

Answer 23

so 3root(x^2)

Answer 24

Nope, the 1's doesn't cancel, \(3\sqrt{x^2-1}-1\neq3\sqrt{x^2}\).

Answer 25

oh woops

Answer 26

can it be simplified then?

Answer 27

Nope

Answer 28

ah ok then e can be simplified?

Answer 29

Yeah, since the f(x) takes away the square-root sign of g(x).

Answer 30

\(f(g(x))=f(\sqrt{x^2+1})=(\sqrt{x^2+1})^2=x^2+1\)

Answer 31

Then you can put \(h(x)\) into that.

Answer 32

should I multiply out the squared part or just leave it?

Answer 33

looks simpler to just leave it so (3x - 1)^2 + 1

Answer 34

Yeah, it's a matter of taste, I would probably multiply it out to get the pure polynomial form of it.

Answer 35

ah ok, makes sense.

Answer 36

9x^2 - 6x + 2

Answer 37

Alrighty thanks so much for the help :D

Answer 38

No problem =)