Question

The function h(x)=1/x^2+1 is the result of the composition f(g(x)). If g(x) = x^2+1,what is f(x)? A f(x)=1/square root x B f(x)=1/x C f(x)= 1/x+1 D f(x)=1/x^2+1

Answer 1

Answer:

Option B is correct

Step-by-step explanation:

Given: $h(x)=\frac{1}{x^2+1}$ is the result of the composition $f(g(x))$.

Also, $g(x)=x^2+1$

To find: $f(x)$

Solution:

Take $f(x)=\frac{1}{x}$

Now check whether $h(x)$ is equal to $f(g(x))$ or not.

First find $f(g(x))$

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

Also, $h(x)=\frac{1}{x^2+1}$

Therefore,

$h(x)=f(g(x))$

So,

Option B is correct