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zimovet [89]
3 years ago
13

Im so confused so PLS HHELP !!!!!! ;-;

Mathematics
1 answer:
nlexa [21]3 years ago
7 0

Answer:

Step-by-step explanation:

let -2/3 be the rational number and 9 be the positive real number

according to the given of indices this tis can be written as

9^{-2/3}

(3)^{2*-2/3}

3^{-4/3}

1/3^4/3

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Step-by-step explanation:

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2 years ago
Given r(x) = 11/ (x - 42)
julsineya [31]

For a given function f(x) we define the domain restrictions as values of x that we can not use in our function. Also, for a function f(x) we define the inverse g(x) as a function such that:

g(f(x)) = x = f(g(x))

<u>The restriction is:</u>

x ≠ 4

<u>The inverse is:</u>

y = 4 + \sqrt{\frac{11}{x} }

Here our function is:

f(x) = \frac{11}{(x - 4)^2}

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x - 4 = 0

x = 4

So the only value of x that we need to remove from the domain is x = 4.

To find the inverse we try with the general form:

g(x) = a + \sqrt{\frac{b}{x} }

Evaluating this in our function we get:

g(f(x)) = a + \sqrt{\frac{b}{f(x)} }  = a + \sqrt{\frac{b*(x - 4)^2}{11 }}\\\\g(f(x)) = a + \sqrt{\frac{b}{11 }}*(x - 4)

Remember that the thing above must be equal to x, so we get:

g(f(x)) = a + \sqrt{\frac{b}{11 }}*(x - 4) = x\\\\{\frac{b}{11 }} = 1\\{\frac{b}{11 }}*4 - a = 0

From the two above equations we find:

b = 11

a = 4

Thus the inverse equation is:

y = 4 + \sqrt{\frac{11}{x} }

If you want to learn more, you can read:

brainly.com/question/10300045

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