The function F is defined by f(x) = 3x-5 over x+6 find f(5x)
1 answer:
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(a)
Domain:
we know that domain is all possible values of x for which any function ios defined
Here, curve is defined for all values of x
so, domain is
Range:
Range is all possible values of y for which x is defined
minimum value of y is -4
maximium value of y is +inf
so, range is
(b)
x-intercept:
It is the value of x where f(x)=0
so, the point where curve intersects on x-axis
and we get
and
(c)
Increasing interval:
where curve is moving upward
we can see that
Decreasing interval:
where curve is moving downward
we get
Constant:
constant means horizontal line
there is no horizontal line here
so, it does not exist
(D)
End behavior:
when x-->+inf
y is moving upward
so, y---->+inf
when x-->-inf
y is moving upward
so, y---->+inf
(E)
we can see that curve jupms at x=-1
so, there is discontinuity at x=-1
and this is jump type of discontinuity
(F)
For odd:
f(-x)=-f(x)
For even:
f(-x)=f(x)
we can see that none of them holds true
so, this is neither
If is a number that is both divisible by 4 and 5, then
4 and 5 are coprime, so we can use the Chinese remainder theorem to solve this system and find that is a solution to the system, where
is any integer. Simply put, any multiple of 20 fits the bill.
Now, there are 11 numbers between 100 and 300 that are divisible by 20 (100, 120, 140, and so on). We have when
, so the sum we want to compute is