Functions and Domains~ I need help thanks

[koreanstar88]

23. f(x) = 4/(x+1)
g(x) = 1/(6-x)

Find the domain of f, g, f+g, f-g, fg, ff, f/g, and g/f.

Find (f+g)(x), etc..

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I know how to find the (f+g)(x), (f-g)(x) answers, but I'm confused on how to find the domains of f+g, f-g, fg, etc.. i only know how to find f and g.


Also if they give you a graph of the domain of F and G, how are you supposed to find the domain of F+G?
I F+G is the intersection between F and G, but I'm confused on if there is a certain way to graph F+G? How do you graph F+G, F-G, etc.. based on only F and G?

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Find the domain and range of this function.
2. f(x) = (x-2)^4 + 1


Is the best way to find the domain and range, is to plug in points into the function, and then graph those points? Or is there a particularly easy way to find the domain and range?


THANK YOU PLEASE HELP ASAP!!! i really appreciate ittttt

 

[galactus]

23. f(x) = 4/(x+1)
g(x) = 1/(6-x)

Find the domain of f, g, f+g, f-g, fg, ff, f/g, and g/f.

Find (f+g)(x), etc..

---------
I know how to find the (f+g)(x), (f-g)(x) answers, but I'm confused on how to find the domains of f+g, f-g, fg, etc.. i only know how to find f and g.

When finding domains, the thing to look for is division by 0 and negatives inside radicals. Those will NOT be in the domain.

For instance, \(\displaystyle \L\\f+g=\frac{4}{x+1}+\frac{1}{x-6}=\frac{3x-25}{(x-6)(x+1)}\)

What results in division by 0?. -1 and 6. See?. Everything but those are in the domain.

\(\displaystyle \L\\\frac{f}{g}=\frac{4(x-6)}{x+1}\). OK, what results in division by 0?. That's NOT in the domain.

 

[koreanstar88]

23. f(x) = 4/(x+1)
g(x) = 1/(6-x)

Find the domain of f, g, f+g, f-g, fg, ff, f/g, and g/f.

Find (f+g)(x), etc..

---------
I know how to find the (f+g)(x), (f-g)(x) answers, but I'm confused on how to find the domains of f+g, f-g, fg, etc.. i only know how to find f and g.

When finding domains, the thing to look for is division by 0 and negatives inside radicals. Those will NOT be in the domain.

For instance, \(\displaystyle \L\\f+g=\frac{4}{x+1}+\frac{1}{x-6}=\frac{3x-25}{(x-6)(x+1)}\)

What results in division by 0?. -1 and 6. See?. Everything but those are in the domain.

\(\displaystyle \L\\\frac{f}{g}=\frac{4(x-6)}{x+1}\). OK, what results in division by 0?. That's NOT in the domain.

Also what if the answer of f+g comes out to be something like 2x-3
do i just need to plug in random numbers to see what the domain is or..?


also how would i graph f+g, f-g, just with using the domains of f and g???

 

[galactus]

Obviously, something like 2x-3 has no restrictions on the domain over the reals. No, it's domain would be \(\displaystyle \L\\(-\infty, \infty)\)

As for the graphs, just look at it. Here's the graph of f+g. Notice the vertical asymptotes at -1 and 6?. That's an indication -1 and 6 are not in the domain because it heads off to -infinity and infinity at those points.

 

[koreanstar88]

Obviously, something like 2x-3 has no restrictions on the domain over the reals. No, it's domain would be \(\displaystyle \L\\(-\infty, \infty)\)

As for the graphs, just look at it. Here's the graph of f+g. Notice the vertical asymptotes at -1 and 6?. That's an indication -1 and 6 are not in the domain because it heads off to -infinity and infinity at those points.

But like say I have a graph having only the domains of F and G graphed.
How do I graph F+G, F-G?
Is there a particular way to graph them?
I am still confused sorry.