Question

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.
f(x)=4/x g(x)=4/x

Answer 1

\[f(g(x))=4/(4/x)\]
4/1 * x/4
cancel the 4s so you get x

Answer 2

Since they're the same equation, you've already solved g((f(x)) and know that it's equal to x.

Answer 3

So, x=1?

Answer 4

No. x is equal to both f(g(x)) and g(f(x)) which can be considered in very simple terms the y values. The slope is 1 but x is not.

Answer 5

What I gathered from your question is that you're only trying to prove that f(g(x)) is equal to g(f(x)) and that is done by solving each and comparing the results, both of which are x. Because they match, they're equal and according to your question that makes them inverses.

Answer 6

So g(x) is the same as f(x) they both equal x?

Answer 7

g(x) and f(x) are not equal to x. g(f(x)) and f(g(x)) are equal to x. Do you understand the difference between g(x) and g(f(x))?

Answer 8

no :(

Answer 9

Ok so if f(x) is the function of x and g(x) is a different function of x, f(g(x)) is the function of g(x). In other words, you're using the equation of g(x) to plug in for the x in the original f(x) equation. For example: f(x)=x+2 and g(x)=2x f(g(x))=(2x)+2

Answer 10

So Both f(g(x)) and g(f(x)) are the same so that makes them inverses?

Answer 11

By the definition you gave "Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. f(x)=4/x g(x)=4/x" Yes. According to the question it can be proved that they're inverses if both f(g(x)) and g(f(x)) equal x, which you know they do because you solved both equations.

Answer 12

Thank you so much, you are so smart. :)

Answer 13

No problem! Not smart, just more experience so far. :) Let me know if you need help with anything else.

Answer 14

Can you help me with a graph?

Answer 15

yes

Answer 16

Just tag me in the question post.

Answer 17

Determine if the function is one-to-one

Answer 18

@christina18

Answer 19

A function for which every element of the range of the function corresponds to exactly one element of the domain. In other words if for every x value there is only one y value. You can determine this by doing the vertical and horizontal line tests. Have you heard of them?

Answer 20

That's where it crosses through two or more points on a graph with a horizontal/ vertical line?

Answer 21

That's what they test, correct. Basically if you were to put your pencil flat across the graph horizontally and move it up across the graph and it never touches the graph in more than one place it passes. The vertical line test uses the same process except obviously vertical. To be one to one a graph must pass both tests. Does it?

Answer 22

No, the horizontal line goes through more than one value

Answer 23

Correct, so what does that mean?

Answer 24

It's not a one to one :)

Answer 25

Exactly! Nice job.

Answer 26

Thank you so much :)

Answer 27

No problem.