Inequality where x≠ -1

[Beni]

I am struggling to understand this inequality question. I don’t understand how to generate the final inequality

Q3.a

F(x) =2/x+1
G(x) = 8

x≠ -1

“Find the set of values for x for which the curve with the equation y = f(x) is below the line with the equation y= g(x)”

Help would be much appreciated

 

[Deleted member 4993]

I am struggling to understand this inequality question. I don’t understand how to generate the final inequality

Q3.a

F(x) =2/x+1
G(x) = 8

x≠ -1

“Find the set of values for x for which the curve with the equation y = f(x) is below the line with the equation y= g(x)”

Help would be much appreciated

I believe you wanted to write F(x) = \(\displaystyle \frac{2}{x+1}\) which should be typed as F(x) =2/(x+1)

Those parentheses are very important.

If I were to do this problem for my assignment:

I would graph F(x) and G(x). and determine the required domain for the condition [F(x) < G(x) ] holds true.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

 

[Otis]

the curve with the equation y = f(x) is below the line with the equation y= g(x)”

Hi Beni. If one curve (or partial curve) lies below another curve, then its y-coordinates are smaller. The symbols f(x) and g(x) are the y-coordinates.

For some values of x, the curve of function f is lower than the curve of function g, therefore the values of f(x) must be less than the values of g(x) for those values of x. That's the inequality to solve for x.

?

 

[Beni]

Thanks

 

[Beni]

I believe you wanted to write F(x) = \(\displaystyle \frac{2}{x+1}\) which should be typed as F(x) =2/(x+1)

Those parentheses are very important.

If I were to do this problem for my assignment:

I would graph F(x) and G(x). and determine the required domain for the condition [F(x) < G(x) ] holds true.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

I have the answer x>0.75 however I am unsure what to do with the x ≠ -1

 

[Dr.Peterson]

I have the answer x>0.75

That's part of the answer (if you correct the sign), but there's more.

Can you show your work?

however I am unsure what to do with the x ≠ -1

I'm not sure where it fits into the problem itself. Can you show us exactly what the problem you are working on said?

As I imagine it, they may be just explicitly mentioning the domain of F, and there is nothing special you need to do with it.

 

[Otis]

Hi Beni. Are you familiar with any of the following?

Basic graph shape y=1/x

Asymptotes

Horizontal shifts of function graphs

If so, we can use those things to better understand the exercise.

?