Question

Find f(x) and g(x) so the function can be expressed as y = f(g(x)). (1 point)

Answer 1

Answer:

$f(x)=x+4$

$g(x)=\frac{8}{x^2}$

Step-by-step explanation:

we are given

we are given

$y=\frac{8}{x^2}+4$

Since, we have to  identify f(x) and g(x)

where g(x) is inner function

Let's assume

$g(x)=\frac{8}{x^2}$

so, we get

$y=g(x)+4$

we know that

y=f(g(x))

so, we can also write as

$f(g(x))=g(x)+4$

now, we can replace g(x) as x

we get

$f(x)=x+4$

so, we get

$f(x)=x+4$

$g(x)=\frac{8}{x^2}$

Answer 2

Answer:

$g(x)=x^2+4$ and $f(x)=\frac{8}{x}$

Step-by-step explanation:

If we want to express $y$ as $y=f(g(x))$, this means that put the function $g(x)$ into $x$ of $f(x)$ to get $y$.

The function $y$ is given as $y=\frac{8}{x^{2}+4}$

So we need to figure out a function $g(x)$ that we can put into another $f(x)$ to get $y$

If we let $g(x)=x^2+4$ and $f(x)=\frac{8}{x}$, we can clearly see that putting g(x) into x of f(x) will give us  $\frac{8}{x^2+4}$, which is y.

Hence $g(x)=x^2+4$ and $f(x)=\frac{8}{x}$