Question

Given f(x)=x3 and g(x)= 1-5x2, fine (fog)(x) and it’s Domain

Answer 1

Answer:

Option B. $f(g(x)) = (1-5x ^ 2) ^ 3$  all real numbers

Step-by-step explanation:

We have

$f(x) = x ^ 3$ and $g(x) = 1-5x ^ 2$

They ask us to find

(fog)(x) and it's Domain

To solve this problem we must introduce the function g(x) within the function f(x)

That is, we must do f(g(x)).

So, we have:

$f(x) = x ^ 3$

$g(x) = 1-5x ^ 2$

Then:

$f(g(x)) = (1-5x ^ 2) ^ 3$

The domain of the function f(g(x)) is the range of the function $g(x) = 1-5x ^ 2$.

Since the domain and range of g(x) are all real numbers then the domain of f(g(x)) are all real numbers

Therefore the correct answer is the option b: $f(g(x)) = (1-5x ^ 2) ^ 3$

And his domain is all real.

Answer 2

Answer:

The correct choice is B

Step-by-step explanation:

The composite function (f o g)(x) is evaluated by substituting g(x) in place of x in f(x) which yields; (f o g)(x) = (g(x))^3 which finally becomes; (1-5x^2)^3. This function clearly is not a rational function and as such it has no undefined points nor domain constraints. It is defined and real for every value of x.