Question

Please help me with this hard problem

Answer 1

Part 1: Finding $(g\circ h)(x)$

Note that $(g\circ h)(x)=g(h(x))$

In this case, it is $g(\sqrt{x+4})=(\sqrt{x+4})^{2}-3=x+4-3=\boxed{x+1}$

Part 2: Domain

For the domain, we need to make sure the radicand of h(x) is greater than or equal to 0, so we get $x+4 \geq 0 \longrightarrow \boxed{x \geq -4}$

Answer 2

The composition (g ο h) = x+ 1 and the domain of the composition (g ο h) is = (-∞ , ∞).

The composition (g ο h) means that the function g(x) composes of h(x) that is g(h(x)). So we have to put the the values of h(x) in the function g(x).

Now here it is given that

g(x) = $x^{2} -3$ and h(x) = $\sqrt[2]{x + 4}$

so to get (g ο h) we have to replace the x with the value of h(x)

That gives :

g(h(x)) = $\sqrt[2]{x+4} ^{2} - 3$

g(h(x)) = x + 4 - 3 = x +1

So the composition (g ο h) = x+ 1

The domain of the function is the values of x for which the function is defined.

so the domain of the composition (g ο h) is :

g(h(x)) = x+ 1

This function is undefined for no value of x .

So its domain is (-∞ , ∞).

Learn more about composition and domain here -https://brainly.com/question/13463273

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