Question

Given f(x) =1/(x^2+4) and g(x) = square root (x+1) Find g(f(x)).

Answer 1

Explanation:

all steps are in the picture above.

Note:if you have any question let me know about.thanks

Answer 2

9514 1404 393

Answer:

g(f(x)) = √((x²+5)/(x²+4))

Explanation:

`g(f(x))=g((1)/(x^2+4))=\sqrt{(1)/(x^2+4)+1}=\sqrt{(1+x^2+4)/(x^2+4)}\\\\\boxed{g(f(x))=\sqrt{(x^2+5)/(x^2+4)}}`

I prefer this compact form, but some may want the denominator rationalized. This means the expression becomes ...

`g(f(x))=\sqrt{((x^2+5)(x^2+4))/((x^2+4)^2)}\\\\\boxed{g(f(x))=(√(x^4+9x^2+20))/(x^2+4)}`