Question

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

Answer 1

Answer:

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

Step-by-step 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) = $\frac{(5+x)(5-x)}{x+5}$

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

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

Answer 2

Answer:

$\frac{f(x)}{g(x)} = (5-x)$

Step-by-step 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

$\frac{f(x)}{g(x)} = \frac{25-x^2}{x+5}$

WE factor 25-x^2

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

$\frac{f(x)}{g(x)} = \frac{25-x^2}{x+5}$

$\frac{f(x)}{g(x)} = \frac{(5-x)(5+x)}{x+5}$

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

$\frac{f(x)}{g(x)} = (5-x)$