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Given:
To find:
Whether f(x) and g(x) are inverse of each other by using that f(g(x)) = x and g(f(x)) = x.
Solution:
We know that, two function are inverse of each other if:
and
We have,
Now,
Similarly,
Since, and
, therefore, f(x) and g(x) are inverse of each other.
Answer:
Formula for the Arc length is given by:
As per the statement:
radius of circle(r) = 6 units
Angle () =
radian
Use conversion:
=
then;
substitute these given values we have;
Use value of
or
Simplify:
Therefore, the arc length of the arc substended in a circle with radius 6 units an angle of 7 pi/8 is 16.485 units