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For the real-valued functions g(x)=(x-4)/(x-5) and h(x)=4x+1 . find the composition gcirc h and specify its domain using interval notation. (gcirc h)(x)=square Domain of gcdot h:square

Pergunta

For the real-valued functions g(x)=(x-4)/(x-5) and h(x)=4x+1 . find the composition
gcirc h and specify its domain using interval notation.
(gcirc h)(x)=square 
Domain of gcdot h:square

For the real-valued functions g(x)=(x-4)/(x-5) and h(x)=4x+1 . find the composition gcirc h and specify its domain using interval notation. (gcirc h)(x)=square Domain of gcdot h:square

Solução

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PriscilaElite · Tutor por 8 anos

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To find the composition
, we need to substitute
into
.

Given:



Substituting
into
:


The domain of
is the set of all real numbers except for the values that make the denominator zero. In this case, the denominator is
, which is zero when
. Therefore, the domain of
is all real numbers except
.

In interval notation, the domain of
is
.
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