Find the domain of the coposite function f∘g f(x)=5x+9 g(x)=x+6

The value of f∘g is: f(g(x))=f(x+6) =5(x+6)+9 =5x+15 therefore the composite function fog is:f(g(x))=5x+15 as we know that the domain of the function is the set of values of the independent variable for which the function is defined. so we can notice that the composite function f∘g is defined when the denominator of f∘g is not equal to zero. that implies x+15≠0 x≠−15 therefore the composite function f∘g is defined for all values of x except x=-15. therefore the domain of the composite function f∘g is :{x∣x≠−15} therefore the second option is correct.

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Falak Kinney

Answered question

2020-11-24

Find the domain of the coposite function $f \circ g$
$f (x) = \frac{5}{x + 9}$
$g (x) = x + 6$

Answer & Explanation

faldduE

Skilled2020-11-25Added 109 answers

The value of

f \circ g

is:

f (g (x)) = f (x + 6)

= \frac{5}{(x + 6) + 9}

= \frac{5}{x + 15}

therefore the composite function fog is:

f (g (x)) = \frac{5}{x + 15}

as we know that the domain of the function is the set of values of the independent variable for which the function is defined.
so we can notice that the composite function

f \circ g

is defined when the denominator of

f \circ g

is not equal to zero.
that implies

x + 15 \neq 0

x \neq - 15

therefore the composite function

f \circ g

is defined for all values of x except x=-15.
therefore the domain of the composite function

f \circ g

: {x ∣ x \neq - 15}

therefore the second option is correct.

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