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3 years ago

Let f(x) = log2(x) and g(x) = 2x.

Mathematics

1 answer:

zzz [600]3 years ago

6 0

Answer:

a) f(g(x)) = 1 + log₂(x)

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)

f(g(x)) = 1 + log₂(x)

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

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$\bf 16sin^5(x)+2sin(x)=12sin^3(x)
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\stackrel{common~factor}{2sin(x)}[8sin^4(x)+1-6sin^2(x)]=0\\\\
-------------------------------\\\\
2sin(x)=0\implies sin(x)=0\implies \measuredangle x=sin^{-1}(0)\implies \measuredangle x=
\begin{cases}
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\end{cases}\\\\
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