Heres the problem: g(f(3))

g(x)=x−1 / 2 and f(x)=2x+1

Question

Heres the problem: g(f(3))

g(x)=x−1 / 2 and f(x)=2x+1

anonymous · Answer

no

anonymous · Answer

Sorry guys. I solved this before and it didnt copy properly.

anonymous · Answer

-5

anonymous · Answer

I'm solving it again.

anonymous · Answer

okay

anonymous · Answer

You would want to apply the f function and then the g fxn.
So you start with 
f(x)=2x+1 and then make that x in 
g(x)=x−12 so 
g(f(x))=(2x+1)−12
and then you would substitute x for 3 and solve.

anonymous · Answer

The other way would be to solve through the process like so:
2x+1 --> 2(3)+1= 7
x=7
x-12 --> 7-12= g(f(x))= -5

anonymous · Answer

$$\frac{ 2(3) + 1 }{ 2 } - 1$$

$$\frac{ 6 + 1 }{ 2 } - 1$$

$$\frac{ 7 - 1 }{ 2 }$$

$$\frac{ 6 }{ 2 }$$

= 3

anonymous · Answer

Did I do something wrong?

anonymous · Answer

@Grazes ... I was wrong. Lol. Im going to compare answers now to see what I did wrong.

anonymous · Answer

It would help if you told me where you got $$\frac{ 2(3)+1 }{ 2 } -1$$ from.

anonymous · Answer

@Grazes  the entire question came out wrong because of an error on openstudy. Dont know why. Im going to retype the question here:

Heres the actual QUESTION:

Let f(x) = 2x + 1 and g(x) = x-1 / 2 find: g(f(3))

anonymous · Answer

Your answer is right.

anonymous · Answer

But your work is partially wrong. Check your first and 2nd expressions. the -1 should be in the fraction.

anonymous · Answer

Also, you should get into the habit of finding the g(f(x)) first because it helps a lot with harder problems with intensive calculation
((2x+1)-1)/2
2x/2=x
x=3 and you're finished.

anonymous · Answer

oooooh !!!

Hey @Grazes Im going to tag you in another. Can you tell me if I am correct when I do? Possibly I can put it below and tag you?

anonymous · Answer

If it's going to be in this post, you need not tag me, but sure.

anonymous · Answer

Problem:

Let f(x) = 2x +1 

$$g(x)=\frac{ x-1 }{ 2 }$$

Find: f(g(x))

$$\frac{ 2(x-1) + 1}{ 2 }$$

$$\frac{ 2x - 1 + 1 }{ 2 }$$

$$\frac{ x - 1 + 1 }{ ? }$$

$$x + 0$$

$$= x$$

anonymous · Answer

Did I do that correctly?

anonymous · Answer

Yes. Also, I read the first problem incorrectly.

anonymous · Answer

The first one should have been
$$2(\frac{ x-1 }{ 2 })+1$$
$$(x-1)+1 = x$$
The answer would be the same, though.

anonymous · Answer

Ohhhh, so I just need to work on organizing my problem easier for understanding and easy solving.

anonymous · Answer

Just don't get confused.

anonymous · Answer

Thanks so much ! @Grazes