Suppose-that-f-x-1-x-1-and-g-x-4-x-1-Find-the-domain-of-each-of-the-composition-a-f-o-g-b-f-o-f-

Question Number 10887 by Saham last updated on 28/Feb/17

Suppose that f (x) = \frac{1}{x + 1} and g (x) = \frac{4}{x + 1} .

Find the domain of each of the composition

(a) f o g (b) f o f

Answered by geovane10math last updated on 28/Feb/17

I wrote an answer

Commented by geovane10math last updated on 28/Feb/17

f (x) = \frac{1}{x + 1} g (x) = \frac{4}{x + 1}

a f (g (x)) = f (\frac{4}{x + 1}) = \frac{1}{\frac{4}{x + 1} + 1}

Domain : \frac{4}{x + 1} + 1 \neq 0

\frac{4}{x + 1} \neq - 1

\frac{4}{- 1} \neq x + 1

- 4 \neq x + 1

x \neq - 5

b f (f (x)) = f (\frac{1}{x + 1}) = \frac{1}{\frac{1}{x + 1} + 1}

Domain : \frac{1}{x + 1} + 1 \neq 0

\frac{1}{x + 1} \neq - 1

\frac{1}{- 1} \neq x + 1

- 1 \neq x + 1

x \neq - 2

Commented by Saham last updated on 28/Feb/17

i did not see it sir .

Commented by Saham last updated on 28/Feb/17

I really appreciate your effort sir . God bless you .

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