Question

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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Answer 1

Answer:

{x ∈ R ∣ x ≠ 4/5}

Explanation:

Answer 2

domain is set of all real number except 4/5

Explanation:

`f(x)= (x-3)/(x)`

`g(x)=5x-4`

Now we find (fºg)(x)

(fºg)(x)=f(g(x))

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

`f(g(x))=f(5x-4)= ((5x-4)-3)/(5x-4)`

Now simplify the numerator

`f(g(x))=((5x-4)-3)/(5x-4)=(5x-7)/(5x-4)`

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

`5x-4=0`

Add 4 on both sides

`5x=4`

Divide both sides by 5

`x=(4)/(5)`

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