3 years ago

(64/125) to the power of -2/3

1 answer:

7 0

As the exponent is negative, we can rewrite the expression as (125/64) raised to the power 2/3.

So, (125/64) raised to the power 2/3 can also be written as [(5/4) raised to the power 3] raised to the power 2/3. The exponents will multiply and the final exponent will be 2.

Hence the answer will be (5/4) squared.
Therefore the answer is (24/16).

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Based on the graphs of f (x) and g(x), what must the domain of (f ⋅ g)(x) be?

bekas [8.4K]

Using the concept of domain, the domain of (f.g)(x) is given by:

{x ∈ ℝ | x ≠ 3}

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The domain of a function is given by all possible input values, that is, <u>on a graph, all values that the x-axis assumes.</u>
In the graph, <u>function f assumes all real values.</u>
Function g is not defined for x = 3, thus, it's domain is all real values except 3.
Thus, the multiplication, as $fg(x) = f(x) \times g(x)$ , will also not be defined at x = 3, and the domain of the multiplication is: