Question

f(x) = 2x + 5, g(x) = X - 5 / 2

A. Graph the functions f(x) and g(x) on the same coordinate plane. You may use technology to create the graph of the functions or submit a handwritten graph.

B. In two or more complete sentences, explain how to use the graphs of f(x) and g(x) to prove that the functions are inverses of each other.

I don't understand what it is I have to do.

Answer 1

First you would plot these two functions....Were you able to do this?

Answer 2

f(x) is blue g(x) is orange.

Answer 3

Would they be inverses of each other because they end up going in opposite directions of the coordinate plane?

Answer 4

So so sorry Im trying to refresh on finding inverse....

Answer 5

It's okay.

Answer 6

You're helping me so there really is no need to apologize.

Answer 7

You would need to use...

\(\huge{f(g(x))=g(f(x))=x}\)

So we would substitute x for the opposite equation....

So lets do `f(x)` first...

We have \(\huge{f(x)=2x+5}\) Now we substitute `g(X)` for x....

\(\huge{f(x)=2(x-\frac{5}{2})+5}\)

Simplify...

Answer 8

\[2x - 2\frac{ 5 }{ 2 } (im assuming) + 5\]

Answer 9

*im assuming

Answer 10

I actually got \(\Large{f(x)=2x}\)

Answer 11

oh. How did you get that?

Answer 12

Wait is it \(\Large{g(x)=\frac{x-5}{2}}\) or is it the way I have been writing?

Answer 13

it's \[g(x) = \frac{ x - 5 }{ 2 }\]

Answer 14

OOOOOoooo well then I though it was the other way cause you didnt put parenthesis so I didnt know sorry

Answer 15

My fault, sorry.

Answer 16

So our equation is....

\(\huge{f(x)=2(\frac{x-5}{2})+5}\)

So 2 multiplied by a fraction of 2 cancels out the two... and 5 (fractions) added by 5 cancels so....

\(\huge{f(x)=x}\)

Answer 17

I would be left with f(x) = \[\frac{ x }{ 2 }\] right?

Answer 18

Not quite.