Destinyyyy
  • Destinyyyy
Help with two problems..
Mathematics
katieb
  • katieb
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Destinyyyy
  • Destinyyyy
Given f(x)= 3+2/x and g(x)= 1/x find f_g, f-g, fg, and f/g. Determine the domain for each function.
Destinyyyy
  • Destinyyyy
I only need help with the last one. f/g. I got 3x+2/1 the system is telling me its correct but not fully simplified.
Destinyyyy
  • Destinyyyy

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Destinyyyy
  • Destinyyyy
Nnesha
  • Nnesha
f(x) divide by g(x) \[\huge\rm \frac{ \frac{ 3+2 }{ x } }{ \frac{ 1 }{ x } }\] now solve
Nnesha
  • Nnesha
combine like terms first and then multiply top with the reciprocal of the bottom fraction
Destinyyyy
  • Destinyyyy
Sorry the site wouldnt load to let me back in..
Destinyyyy
  • Destinyyyy
Huh? I have 3x+2/ 1
Nnesha
  • Nnesha
\(\color{blue}{\text{Originally Posted by}}\) @Destinyyyy Given f(x)= 3+2/x and g(x)= 1/x find f_g, f-g, fg, and f/g. Determine the domain for each function. \(\color{blue}{\text{End of Quote}}\) f(x) is 3+2/1
Destinyyyy
  • Destinyyyy
?
Destinyyyy
  • Destinyyyy
The 1 is under 3x+2
Destinyyyy
  • Destinyyyy
I need to simplify that further so how.
Nnesha
  • Nnesha
well the question u posted above is f(x) = 3+2/x
Nnesha
  • Nnesha
please rewrite f(x) and f(x) function
Destinyyyy
  • Destinyyyy
What? f(x)= 3+ 2/x g(x)= 1/x some*
Destinyyyy
  • Destinyyyy
the x is only under the 2.
Destinyyyy
  • Destinyyyy
3+ 2/x over 1/x * x/x = 3x+2 all over 1
Nnesha
  • Nnesha
alright \[\huge\rm \frac{ 3+\frac{ 2 }{ x } }{ \frac{ 1 }{ x } }\] equal \[\frac{\frac{ 3x+2 }{ x } }{ \frac{ 1 }{ x } } = \frac{ 3x+2 }{ x } \times \frac{ x }{ 1 } = 3x+2\] that's it
Nnesha
  • Nnesha
that's simplified !
Destinyyyy
  • Destinyyyy
Alright. Thank you. For f(x)= 2x-5 and g(x)= 4x^2 -4 D. (g*f)(1)
Nnesha
  • Nnesha
according to the previous post i guess * means compose like (g o f)(1) so first find f(1) substitute x for 1 into f(x) function or in other words you have to find g(f(1))
Nnesha
  • Nnesha
but if it's a multiplication sign then it would be f(1) times g(1)
Destinyyyy
  • Destinyyyy
Yes the o thing.
Nnesha
  • Nnesha
ye thats what i asked n the previous post (f * g)(x) isn't same as (f o g)(x) ^multiplication ^substitution
Nnesha
  • Nnesha
( g o f)(1) = g -compose -f of 1
Destinyyyy
  • Destinyyyy
Yeah sorry about that. Its super tiny on my screen so I assumed it was *
Nnesha
  • Nnesha
its okay :=)
Destinyyyy
  • Destinyyyy
1 Attachment
Nnesha
  • Nnesha
so for this question find (g o f )(1) = g(f(1)) substitute x for 1 into f(x) function then plugin the result into g(x) function
Destinyyyy
  • Destinyyyy
The picture shows the example I have.
Nnesha
  • Nnesha
alright so in the example first they solvved g(f(x) and then sub x for 1
Destinyyyy
  • Destinyyyy
So 4(2x-5)^2 -4 ?
Nnesha
  • Nnesha
looks good
Destinyyyy
  • Destinyyyy
That all turns into 16x^2 -80x +96
Destinyyyy
  • Destinyyyy
And I just plug 1 in for x correct?
Nnesha
  • Nnesha
alright i'll trust the calculator yes right now replace x with 1
Destinyyyy
  • Destinyyyy
Final answer 32
Nnesha
  • Nnesha
right
Destinyyyy
  • Destinyyyy
Thank you.
Nnesha
  • Nnesha
yw

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