## 155 Reputation

6 years, 208 days

## the problem came up...

The problem came up when I was asked to compose two functions and determine if the composed function is one to one, onto, or neither.

Full link to the question :

http://s3.amazonaws.com/chegg.media.images/board/904/904d6355-379d-4de3-91e1-0dc8926f99f3-original.png

I defined h(x) = x^4, g(x) = surd(x,8).

I wanted to show that the composition f=h(g(x)) is not onto by showing there is no solution

to h(g(x) = -2.

The root[] command might be better for solving equations than the surd.

Here is a screenshot, with both surd and rational exponents for comparison.

The root[8](x) command gives me the expected response of no solution.

Should I just stick with rational exponents?

It would be nice if Maple would say 'no solution' when there is no result.

Otherwise someone might think their version of Maple is buggy or something.

Also I notice Maple does not simplify exponents by default. For example (x^4)^(1/8) does not become x^(1/2).

One way seems to be to make an assumption.

## @broe I would define new trig funct...

I would define new trig functions by appending the letter d to the default trig functions, which accept degrees as arguments for sin,cos, tan,etc. and output degrees for the inverse trig functions.

sind:=d->sin(Pi/180*d):
cosd:=d->cos(Pi/180*d):
tand:=d->tan(Pi/180*d):
cscd:=d->csc(Pi/180*d):
secd:=d->sec(Pi/180*d):
cotd:=d->cot(Pi/180*d):
arcsind:=y->180/Pi*(arcsin(y)):
arccosd:=x->180/Pi*(arccos(x)):
arctand:=m->180/Pi*(arctan(m)):
arccotd:=a->180/Pi*(arccot(a)):
arcsecd:=b->180/Pi*(arcsec(b)):
arccscd:=c->180/Pi*(arccsc(c)):

To see the result,  https://i.imgur.com/cpxzzMK.png

## Oh I feel so ......

Thanks guys. I didnt realize I forgot the colon when I defined L.

And yes, I meant it to be an ordered list, check f(1) = h(1), then f(2) = h(2), etc.

Let me use different numbers to clear up ambiguity.

I have two sets

f:={8,9,6,7}; h:={8,9,7,6} ; L=seq(i,i=1..4):

for i in L do
if f[i]=h[i] then
print(f[i]);
end if;
end do;

The output should be {8,9}.

So it doesn't make a difference if you use {}  or [ ], when we define f,h.

Can anyone recommend me a maple programming guide, for newbies?

@Preben Alsholm Thanks for the reply. I will have to do some research to understand these terms. Do you have a suggestion for learning Maple more in depth

## looks like a good book...

I might want to buy this.

## what is going on here...

@Preben Alsholm what is going on internally here. nothing seems to happen here

According to this, it uses a remember table

https://en.wikibooks.org/wiki/Maple/Getting_Started#Defining_a_function_with_Maple

> f(x):=2*x+2;


defines f as a procedure with a "remember table" that is assigned only for the argument x:

> f(u);

$\mathrm{f}(u)\,$

and

> f(x)=2*x+2;



is an equation.

## interesting...

@Preben Alsholm And based on your example, we could say, evaluating functions comes before exponentiating (order of operations).

That is, x^2(3) = x^(2(3)) = x^(2) = x^2

So to answer the question above

> f:=x^2
> f(3)
why is output: x(3)^2

It is treating 'x' as a function, which we could have defined earlier.

In other words, f(3) = (x(3))^2 = x(3)^2

The only way to escape this is to insert a multiplication sign.

It is interesting that 2(3) evaluates to 2 treating it as a constant function. A proviso, this must be in maple input. In 2d math mode, 2(3) is assumed to be multiplication and evaluates to 6.

## I see the product line. thanks...

@Markiyan Hirnyk woops, i see now. thanks :)

## @Markiyan Hirnyk Sorry I don't understan...

@Markiyan Hirnyk I don't understand.

## Interested...

I an interested to see how Maple can help students learn new concepts.

In my experiencing using Maple lets you avoid tedious calculation so you have a clear idea of the target solution. It can also aid in the understanding of the manual calculations.

## i find it annoying as well...

I have noticed that autoscroll does not work as well in maple 2015

also when i use autocomplete, it gets stuck

For example if I type

with(Student[VectorCalculus]

the cursor gets suck after the letter s and have to manually use mouse to get cursor after ] to close with parentheses.

This only happens in 2d math mode, not in 1d math mode.

But the 1d math mode does not always autoscroll down so I prefer not to use it either.

## i see thankyou...

i see, thankyou

and by 'parsed' what do you mean, that the software adds the smart operator?

im not familiar with this word

## ok is it called maple notation, see imag...

ok is 1d math the same as maple notation http://prntscr.com/8vjur5

and 'maple input' http://prntscr.com/8vjv41

what is the advantage of using maple input versus 2d math

## @vv I am using 1d math , I believe....

I am using 1d math , I believe.

well it says 2d input in the drop down menu

how do you use 1d math.

http://prntscr.com/8vjqs9

## wow that did the trick...

wow that did the trick

I unchecked 'smart operator' and applied globally. now it works.

so the smart operator treated 'D(f)(x)' as D(f)*(x)

still i wonder why with 'smart operator' enabled, it adds a space when you type D(f)(x) into the prompt,

so I see  D(f)  (x)

this might be a clue http://prntscr.com/8vjsxx

if you put a space between (x-3)  (x-2) , maple treats it like (x-3)*(x-2)

without a space it treats it as , something else

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