Evaluate the composition of functions.

Mathematics

1 answer:

valina [46]2 years ago

7 0

Answer:

Step-by-step explanation:

Fill in each function's argument and do the arithmetic.

$h(g(f(\sqrt{10})))=h(g(2(\sqrt{10})^2-7))=h(g(2\cdot 10-7))=h(g(13))\\\\=h(\dfrac{4-13}{9})=h(\dfrac{-9}{9})=h(-1)\\\\=\sqrt{-(-1)+3}=\sqrt{4}=\boxed{2}$

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Which expression is equivalent to 3√32x^8y^10?

denpristay [2]

<span>
3√(32x^8y^10)
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6 0

3 years ago

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please help! functions and relations. f(x)= square root of x-4. find the inverse of f(x) and it’s domain.

likoan [24]

ANSWER:

$\:D.\text{ }f^{-1}\left(x\right)=\left(x+4\right)^2;x\ge-4$

STEP-BY-STEP EXPLANATION:

We have the following equation:

$f(x)=\sqrt{x}-4$

The inverse is the following (we calculate it by replacing f(x) by x and x by f(x)):

$\begin{gathered} x=\sqrt{f^{-1}(x)}-4 \\ \\ \sqrt{f^{-1}(x)}=x+4 \\ \\ f^{-1}(x)=(x+4)^2 \end{gathered}$

The domain would be the range of the original equation, and it would be the range of values that f(x) could take, which was from -4 to positive infinity, that is, f(x) ≥ -4.

Therefore, the domain is x ≥ -4.

So the correct answer is D.