Which is bigger -6 1/3 or -6.375

Mathematics

1 answer:

levacccp [35]2 years ago

5 0

-6 1/3 because it looks less than -6.375 which would mean that it is in fact bigger on the number scale.

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I need help with number 4

ss7ja [257]

Answer: Choice D

$f^{-1}(x) = (x-3)^2+2\\\\$

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Explanation:

First we replace f(x) with y. This is because both y and f(x) are outputs of a function.

To find the inverse, we swap x and y and solve for y like so

$y = \sqrt{x-2}+3\\\\x = \sqrt{y-2}+3 \ \text{ .... swap x and y; isolate y}\\\\x-3 = \sqrt{y-2}\\\\(x-3)^2 = y-2 \ \text{ ... square both sides}\\\\(x-3)^2+2 = y\\\\y = (x-3)^2+2\\\\f^{-1}(x) = (x-3)^2+2\\\\$

Note: because the range of the original function is $y \ge 3$ , this means the domain of the inverse is $x \ge 3$ . The domain and range swap roles because of the swap of x and y.

As the graph shows below, the original and its inverse are symmetrical about the mirror line y = x. One curve is the mirror image of the other over this dashed line.