Describe what homologous structures are and give an example.

1 answer:

7 0

A homologous structure is a structure or organ that can be found on many different animals that suggest that there is a common ancestor. It can be anywhere from a bone to a flap of skin to an organ. A common one to look at is the similarity between a human hand, bat’s wing, whale anterior flipper, and a cat’s paw. All of these have a common, 5-point structure to the bones which suggests that we all come from an animal that had 5 fingers.

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why must the symbol +- be written in front of the radical to write the inverse of the function f(x)=x^2?

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Here is why:

When we solve for the inverse function (see the particular step below; when we have: " y² = x " ;

We take the "square root" of EACH SIDE of the equation; to isolate "y" as a single variable on one side of the equation;

→ √(y²) = √x ;

→ |y| = |√x| ;

y = ± √x ;

Because when we take the square root — or any "even root", for that matter—we have two solutions: of a variable, we have TWO SOLUTIONS: a positive value; and a negative values;

→ since: 1) a "negative value"; multiplied by a "negative value" ; equals a "positive value" ;
→ and as such: a "negative value" ;
multiplied by that same "negative value" ;
{that is: a "negative value", "squared (i.e "raised to the power of "2"} ; ,
→ results in a positive value ;
→ and since:
2) a "postive value"; multiplied by a positive value" ; equals a "positive value" ;
→ and as such: a "positive value" ;
multiplied by that same "positive value" ;
{that is: a "positive value", "squared (i.e "raised to the power of "2"} ; ,
→ results in a "positive value";
→ and since:
3) any given integer, in it "positive value", squared (i.e. raised to the power of "2"); results in a "positive value" ;
→and since:
4) that same aforementioned integer; in its "negative value" form, squared (i.e. raised to the power of "2"); results in that same aforementioned "positive value".
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Note the following:
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"Given the function: "f(x) = x² " ; Find the "inverse function" .

Let "y" = f(x) " ;

and write as: " f(x) = y = x² " ;

→ " y = x² " ;

→ Now, rewrite the equation; replacing the "y" with "x" ;
and replacing the "x" with "y" ;

→ " x = y² " ;

Now, rewrite the question; isolating "y" as a single variable;
with no coefficient (save for the "implied coefficient of "1" ) ;

→ " x = y² " ;

↔ " y² = x ;

Now, take the square root of EACH SIDE of the equation;
to isolate "y" on one side of the equation;

→ √(y²) = √x ;

→ |y| = |√x| ;

→ y = ± <span>√x .
</span>
Replace the "y" with " f ⁻¹(x)" ; to indicate that this the "inverse function" ;

and write the "inverse function" :

→ " f ⁻¹(x) = ± √x " ;
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