Question

If f(x)=25-x^2 and g(x)=x+5, what is (f/g)(x)?

Write your answer in simplest form.

When f(x)=25-x^2 and g(x)=x+5, (f/g)(x)= _______

Answer 1

f/g)(x)= -x+5 or 5-x

Explanation:

We have been given the functions as:

`f(x)=25-x^(2)`

`g(x)=x+5`

We have to find (f/g)(x)

We know that
`a^(2) - b^(2) = (a+b)(a-b)`

So,
`25-x^(2)` =
`(5+x)(5-x)`

(f/g)(x) =
`((5+x)(5-x))/(x+5)`

The (x+5)' are common so they get cancelled out.

Therefore, we get f/g)(x)= -x+5 or 5-x

Answer 2

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

Explanation:

f(x)=25-x^2 and g(x)=x+5

We need to find (f/g)(x)

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

we divide f(x) by g(x) and then we simplify

`(f(x))/(g(x)) = (25-x^2)/(x+5)`

WE factor 25-x^2

25-x^2 = 5^2 - x^2 = (5-x)(5+x)

`(f(x))/(g(x)) = (25-x^2)/(x+5)`

`(f(x))/(g(x)) = ((5-x)(5+x))/(x+5)`

5+x or x+5 are same , so we cancel out x+5

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