Functions: f(x)=1/x-5 g(x)=7/x +5 How do find (fog)(x) and (gof)(x)??

[Aido]

f(x)=1/x-5 g(x)=7/x +5
How do find (fog)(x) and (gof)(x)??

 

[Deleted member 4993]

f(x)=1/x-5 g(x)=7/x +5
How do find (fog)(x) and (gof)(x)??

I assume your problem is:

f(x)=1/(x-5) and g(x)=7/(x +5)

find (fog)(x) and (gof)(x)?

What are your thoughts?

Please share your work with us ...even if you know it is wrong.

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[Aido]

My answer does not simplify any further...

 

[pka]

f(x)=1/x-5 g(x)=7/x +5
How do find (fog)(x) and (gof)(x)??

In your reply numbered 3, you indicate that the functions are really f(x)=1/(x-5) & g(x)=(7/x) +5.
Now tell us why you expected us to know that.

\(\displaystyle f\circ g(x)=f(g(x))=\dfrac{1}{g(x)-5}=\dfrac{1}{\frac{7}{x}}=\dfrac{x}{7}\)

 

[ksdhart2]

If the problem statement asked you to multiply the two functions together [i.e. to find f(x) * g(x)], then you'd be on the right track. However, function composition is not the same thing as multiplication. Rather, you can think of it as evaluating the first function, but with a different parameter. To hopefully get you thinking in the right direction, try working these similar, but simpler exercises.

What would your steps be if you'd been asked to evaluate...

1. \(\displaystyle f(3)\)
2. \(\displaystyle f(775)\)
3. \(\displaystyle f(q)\)
4. \(\displaystyle f(\dfrac{1}{x})\)

Using your results from these exercises, what do you think \(\displaystyle f(\dfrac{7}{x+5})\) would be?

 

[stapel]

\(\displaystyle \left(f\, \circ\, g\right)(x)\,=\, f\left(g(x)\right)\, =\, f\left(\dfrac{7}{x}\, +\, 5\right)\, =\, \dfrac{1}{x\, -\, 5}\, \left(\dfrac{7}{x}\, +\, 5\right)\, =\)

My answer does not simplify any further...

From your sideways image, it appears that you're not familiar with what function "composition" is or how it works. To learn, please try studying some of the lessons listed here.

Once you have studied at least three lessons from the listing, please attempt the exercise again. If you get stuck, please reply with a clear (not sideways, for instance) statement of your efforts so far. Thank you!