Bloom247
13.10.2020 •
Mathematics
One complete period of a sine or cosine graph is given. Write an equation that represents the curve in one of the following forms.
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Ответ:
a) f(g(x)) = 1 + log₂(x)
or
f(g(x)) = 1 + f(x)
b) The function f and g are not inverse functions
Step-by-step explanation:
Data provided:
f(x) = log₂(x)
and,
g(x) = 2x
a) Now,
f(g(x)) = log₂((2x))
also,
we know the property of log function that,
log(AB) = log A + log(B)
therefore,
f(g(x)) = log₂((2x)) = log₂(2) + log₂(x)
or
f(g(x)) = 1 + log₂(x)
or
f(g(x)) = 1 + f(x)
b) f(g(x)) = 1 + log₂(x)
and,
g(f(x)) = 2(log₂(x))
since,
f(g(x)) ≠ g(f(x))
Therefore,
The function f and g are not inverse functions