3 years ago

F ( x ) = ( x - 2 ) ^3

Mathematics

1 answer:

g100num [7]3 years ago

7 0

Answer:

Step-by-step explanation:

f(f^-1(x)) = x

Always!

f(x) = (x - 2)³

y^⅓ = x - 2

x = y^⅓ + 2

f^-1(x) = x^⅓ + 2

f(f^-1(x)) = f(x^⅓ + 2)

= (x^⅓ + 2 - 2)³

= (x^⅓)³

= x

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A right triangle has a perimeter of 24 cm and a hypotenuse of 10 cm. Find the length of the other two sides.

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One of the sides is 6 cm and the other is 8 cm

Step-by-step explanation:

Let's call the unknown sides a and b. From the perimeter information (24 cm) we have:

a + b + hypotenuse = 24

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a + b = 14

b = 14 - a

So now we can right the Pythagorean theorem as follows:

$a^2 + b^2 = hypotenuse^2\\a^2 + (14-a)^2=10^2\\a^2+ 14^2-28\,a+a^2=100\\2\,a^2-28\,a +96=0\\2\,(a^2-14\,a+48)=0\\2\,(a^2-6\,a-8\,a+48)=0\\2(a\,(a-6)-8\,(a-6))=0\\2\,(a-6)\,(a-8)=0$

and from this expression in factor form to be zero a must be 6 or a must be 8.

Therefore the solutions are a = 6 (and therefore b = 14 - 6 = 8)

or a = 8 (and therefore b = 14 - 8 = 6)

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3 years ago

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Crazy boy [7]

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