Question

Expressed powers are those that aref(x) = 5x + 3; g(x) = 6x - 5 Find f/g. (f/g)(x) = Quantity six x minus five divided by five x plus three. domain x (f/g)(x) = Quantity five x plus three divided by six x minus five. domain x (f/g)(x) = Quantity five x plus three divided by six x minus five.domain x (f/g)(x) = Quantity six x minus five divided by five x plus three. domain x

Answer 1

(f/g)(x) = Quantity five x plus three divided by six x minus five.domain x ≠ Five over six.

Step-by-step explanation:

Given functions,

`f(x)=5x+3`

`g(x) =6x-5`

`((f)/(g))(x)=(f(x))/(g(x))`

`=(5x+3)/(6x-5)` ( By substitution )

Let
`h(x)=(5x+3)/(6x-5)`

Which is the rational function,

Since, a rational function is defined for all real number except those for which denominator = 0,

`6x-5=0`

`6x=5`

`x=(5)/(6)`

Thus, h(x) is defined on all real numbers except 5/6,

Hence, domain of
`(f)/(g)(x)` is {x| x ≠
`(5)/(6)` }

Answer 2

Answer: (f/g)(x) = Quantity five x plus three divided by six x minus five.domain x

Step-by-step explanation:

1) (f/g)(x) = f(x) / g(x)

2)

f(x) 5x + 3
-------- = ------------
g(x) 6x - 5

3) Since the division by 0 is not defined, the domain is restricted to 6x - 5 ≠ 0.

Therefore you must solve 6x - 5 = 0 to exclude the value of x for which the denominator becomes 0:

6 x - 5 = 0 => 6x = 5 => x = 5 / 6.

So, the domain is all x | x ≠ 5/6.