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Mathematics: Post your doubts here!

robinhoodmustafa

robinhoodmustafa

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***amd*** said:
the first eq will be p^2 + q^2 = 2^2 (Pythagoras theorem)
second: just substitute p with x and q with y in the eq y = mx + c
Click to expand...
Sorry. I didnot get you.
Can u do the solution for first equation (P^2) one on " sketchtoy.com " and share the link

and this one is a similar question from May June 2014

Screenshot_25.png
 
robinhoodmustafa

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***amd***

What is the method of finding range ? I donot get it at all... Whenever we are given a function, they probably ask us to gives its range while the domain is given

for example if the function is
3x - 2
and domain is −1 ≤ x ≤ 1 so what will be the range? :)
 
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***amd***

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***amd***

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robinhoodmustafa said:
***amd***

What is the method of finding range ? I donot get it at all... Whenever we are given a function, they probably ask us to gives its range while the domain is given

for example if the function is
3x - 2
and domain is −1 ≤ x ≤ 1 so what will be the range? :)
Click to expand...
simply, apply the function f(x) on the max and least values given for domain (in this case, its -1 and +1)

if, for function f:x, domain is -5 < x < 5
then its range is f(-5) < f(x) < f(5)
BUT, for quadratic functions, http://sketchtoy.com/63854982
 
robinhoodmustafa

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***amd*** said:
simply, apply the function f(x) on the max and least values given for domain (in this case, its -1 and +1)

if, for function f:x, domain is -5 < x < 5
then its range is f(-5) < f(x) < f(5)
BUT, for quadratic functions, http://sketchtoy.com/63854982
Click to expand...

Yeah I am aware about quadratic functions.
and what if the equation has a domain of all real values so what will be its range? all real values?

This question. Its about Maximum and minimum. I tried to understand the concept from MS but couldnt get it.


Screenshot_27.png
 
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robinhoodmustafa said:
Yeah I am aware about quadratic functions.
and what if the equation has a domain of all real values so what will be its range? all real values?

This question. Its about Maximum and minimum. I tried to understand the concept from MS but couldnt get it.


View attachment 49634
Click to expand...
i guess Yes, if the domain is all real numbers, the range must be all real. Because you can get an output of a complex number ONLY when you have 'square root' in your function (and square root will quote for TWO values, one +ve and one -ve, which means a SINGLE value of 'x' will give you MORE THAN ONE value of f(x))
there are only 2 types of functions.
1) 1 to 1 function: in which only one value of x quotes only for one distinct value of f(x). e.g. f(x) = 3x + 2, you'll get only Only one distinct value of f(x) for each value of x.
2) Many to one function: in which more than one values of x may quote for same value of f(x). e.g. f(x)= x^2, you can get a single value of f(x) for more than one values of x.
BUT there is no ONE-TO-MANY function, if there is any equation which can give you more than one value of f(x) for one value of x, that can NOT be a function!

hope this helps.
 
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