Question

for f(x)=4x+1 and g(x)=x^2-5, find (f/g)(x)

Answer 1

ANSWER

$( \frac{f}{g} )(x) = \frac{4x + 1}{ {x}^{2} - 5 } .$
where,

$x\ne \pm \sqrt{5}$


EXPLANATION

We were given that

$f(x) = 4x + 1$
and
$g(x) = {x}^{2} - 5$


We are supposed to find
$( \frac{f}{g} )(x)$


Recall that,

$( \frac{f}{g} )(x) = \frac{f(x)}{g(x)}$
We substitute the functions to obtain,

$( \frac{f}{g} )(x) = \frac{4x + 1}{ {x}^{2} - 5 }$


This is a proper rational function and it is in the simplest form.


The restriction is that,

$x\ne \pm \sqrt{5}$

If the denominator is zero the function will be undefined

Answer 2

A function assigns the values. The value of  (f/g)(x) is (4x+1)/(x²-5).

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

Given the function f(x)=4x+1 and the function g(x)=x²-5, therefore, the value of (f/g)(x) will be,

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

           = (4x+1)/(x²-5)

Hence, the value of  (f/g)(x) is (4x+1)/(x²-5).

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