enter image description here This is my working/how I've answered the question. However, does anyone know how I would state the domain of each function using set notation?

My working:

For g(x), the domain is when the inside of the square root is greater than or equal to zero. Thus, x² - 1 ≥ 0 x² ≥ 1 Upon taking the square root of both sides, we result in: x ≥ 1 or x ≤ -1 (the principle square root gets the positive, and the secondary square root gets the negative with the inequality sign flipped).

Thus, this function g(x) has the domain:

{x such that -1 ≥ x ≥ 1 } Or alternatively, {x such that |x| ≥ 1}

With regards to f(x), the domain of the cosine function are all real numbers. The domain of a composite function is the domain which satisfies each individual function.

Thus, the domain of the composite function is: {x such that |x| ≥ 1}

  • 1
    $\begingroup$ It is correct, now do the b)! $\endgroup$ – user90628 Aug 20 '13 at 8:42

If $f,~~g$ are functions such that $f\circ g$ be a function so

$$\text{dom}(f\circ g)\subseteq \text{dom}(g)$$ and $$\text{dom}(f\circ g)=\text{dom}(g)\ \Longleftrightarrow \text{rang}(g)\subseteq \text{dom}(f)$$

  • $\begingroup$ I will give him +1 so that he have 33,333 $\endgroup$ – user90628 Aug 20 '13 at 8:50
  • $\begingroup$ Now, Congratulations 33,333 reputation with 3 kinds of badges including 3 gold one:D $\endgroup$ – Mahdi Khosravi Aug 20 '13 at 8:53
  • 1
    $\begingroup$ @Mahdi Khosrav And his answer has 3 upvotes (at the moment). $\endgroup$ – user90628 Aug 20 '13 at 8:56
  • 1
    $\begingroup$ And all numbers of his badges are divisible by 3. $\endgroup$ – user90628 Aug 20 '13 at 8:58
  • $\begingroup$ +1 & Lots of supportive comments for you dear friend :^) $\endgroup$ – Namaste Aug 21 '13 at 0:27

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.