The domain of f/g
consists of numbers x for which g(x) cannot equal 0 that are in the domains of
both f and g.
Let’s take this equation as an example:
If f(x) = 3x - 5 and g(x)
= square root of x-5, what is the domain of (f/g)x.
For x to be in the domain of (f/g)(x), it must be
in the domain of f and in the domain of g since (f/g)(x) = f(x)/g(x). We also
need to ensure that g(x) is not zero since f(x) is divided by g(x). Therefore,
there are 3 conditions.
x must be in the domain of f:
f(x) = 3x -5 are in the domain of x and all real numbers x.
x must be in the domain of g:
g(x) = √(x - 5) so x - 5 ≥ 0 so x ≥ 5.
g(x) can not be 0: g(x)
= √(x - 5) and √(x - 5) = 0 gives x = 5 so x ≠ 5.
Hence to x x ≥ 5 and x ≠ 5
so the domain of (f/g)(x) is all x satisfying x > 5.
Thus, satisfying <span>satisfy all
three conditions, x x ≥ 5 and x ≠ 5 so the domain of (f/g)(x) is all x
satisfying x > 5.</span>
This equation is written in slope intercept form
Remember that the slope intercept formula is:
y = mx + b
m is the slope
b is the y-intercept
In this case:
slope (m) is 2
y-intercept (b) is (0, - 1)
To plot this on a coordinate plane plot the y-intercept (0, -1).
To graph the rest of the line you can use what you know about the slope. Rise up two units and over to the right one unit from the y-intercept. You should arrive at the point (1, 1)
Then, again from the y-intercept, go down two units and to the left one unit. You should arrive at the point (-1, -3)
Now draw a straight line through the y-intercept and the other two points you just found
The image of the graph is shown below
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
Johannes Gutenberg - Wikipediahttps://en.wikipedia.org › wiki › Johannes_Gutenberg
Johannes Gensfleisch zur Laden zum Gutenberg was a German goldsmith, inventor, printer, and publisher who introduced printing to Europe with his ...
Occupation: Engraver, inventor, and printer
Born: Johannes Gensfleisch zur Laden zum G...
Died: February 3, 1468 (aged about 68); Mainz, ...
Known for: The invention of the movable-type ...
Early life · Printing method with... · Legacy · References
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