f(x) = x2 + 3; g(x) = sqrt(x - 2)

Find f(g(x)).

Question

f(x) = x2 + 3; g(x) = sqrt(x - 2)

Find f(g(x)).

jhannybean · Answer

$$\large f(x) = x^2 +3$$$$\large g(x) = \sqrt{x-2}$$ so replace all the x's in f(x) with the function of g(x).

$$\large f(g(x)) = (\sqrt{x-2})^2 +3 $$
When you square a  square root, the square root and the square cancel eachother out.

jhannybean · Answer

Can you finish solving this now? :)

jhannybean · Answer

They don't necessarily cancel each other out, but when you take the product of two square roots, it becomes an integer.

anonymous · Answer

i might be helpful to take an intermediate step 
maybe not

$$f(g(x))=f(\sqrt{x-2})$$ may help

anonymous · Answer

replace the general $g(x)$ by the specific one you have in this case
then replace the $x$ in $f(x)=x^2+3$ by $\sqrt{x-2}$

anonymous · Answer

also helpful not to think of $x$ when you do this 
$$f(\diamondsuit)=\diamondsuit^2 +3$$ replace $\diamondsuit$ by $\sqrt{x-2}$

anonymous · Answer

x+1 answer