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49.4
if f(x) - x-3/x and g(x) = 5x – 4, what is the domain of (fºg)(x)?
o {1x80}
* {1x^3}
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Respuesta :

Answer:

Answer:

{x ∈ R ∣ x ≠ 4/5}

Step-by-step explanation:

Answer:

domain is set of all real number except 4/5

Step-by-step explanation:

[tex]f(x)= \frac{x-3}{x}[/tex]

[tex]g(x)=5x-4[/tex]

Now we find (fºg)(x)

(fºg)(x)=f(g(x))

We plug in g(x) inside in f(x)

[tex]f(g(x))=f(5x-4)= \frac{(5x-4)-3}{5x-4}[/tex]

Now simplify the numerator

[tex]f(g(x))=\frac{(5x-4)-3}{5x-4}=\frac{5x-7}{5x-4}[/tex]

To find out domain we set the denominator =0 and solve for x

[tex]5x-4=0[/tex]

Add 4 on both sides

[tex]5x=4[/tex]

Divide both sides by 5

[tex]x=\frac{4}{5}[/tex]

So domain is set of all real number except 4/5

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