f(x) and g(x)

[bully3000]

Let and be defined by:





(a) Evaluate , , and .
(b) Find all for which . You must give the exact answer and show all working.

Any help will be appreciated!

[Jaswinder]

just checking my answers?

a)5, -1, -8, -5
b)-0.5 and 4

[bully3000]

just checking my answers?

a)5, -1, -8, -5
b)-0.5 and 4

I don't know what the answers are. SORRY!

[Zealous]

just checking my answers?

a)5, -1, -8, -5
b)-0.5 and 4

Yep, looks like your answers seem correct, I haven't actually come across questions exactly like this, but I can assume you answer it like this.

For , it's just like saying and then subbing in in the place of . Since we know is going to be , we use the bottom part of the hybrid function (because we are subbing in -2 so we see which part of the hybrid function defines x when it is < 0.

So I'll just show you a and d, you can try do b and c yourself.

a)



=

Then sub in x = -2

=
=

d)



Since we are looking at subbing in x when it is 2 (which is > 0), we use the bottom part of the hybrid function.



()

Then you can sub in 2.

= ()

= ()
 
=

If you want me to write out how to do the 2nd part of the question step by step, I can do that later, you just have to equate the equations and solve for x, but you have to take into consideration the hybrid function.
I might have made errors there...  someone else can correct me if I've made mistakes.

[Zealous]

For the second part:
(if you haven't tried and figured it out already.)

Spoiler

You need to find the intersection points of and when x is greater or equal to 0 and the intersection points of and when x is less than 0.

Note this is how I approached this question, there may be other ways.

Equate the first two:


Then solve for x





or
But as we are looking at when x is greater than 0, we cannot have a solution of -1.

So the first solution is

Now we can equate the other two equations:







So the two solkutions are and

[bully3000]

Yep, looks like your answers seem correct, I haven't actually come across questions exactly like this, but I can assume you answer it like this.

For , it's just like saying and then subbing in in the place of . Since we know is going to be , we use the bottom part of the hybrid function (because we are subbing in -2 so we see which part of the hybrid function defines x when it is < 0.

So I'll just show you a and d, you can try do b and c yourself.

a)



=

Then sub in x = -2

=
=

d)



Since we are looking at subbing in x when it is 2 (which is > 0), we use the bottom part of the hybrid function.



()

Then you can sub in 2.

= ()

= ()
 
=

If you want me to write out how to do the 2nd part of the question step by step, I can do that later, you just have to equate the equations and solve for x, but you have to take into consideration the hybrid function.
I might have made errors there...  someone else can correct me if I've made mistakes.

Couldn't check answers with cas calculator...

[bully3000]

Yep, looks like your answers seem correct, I haven't actually come across questions exactly like this, but I can assume you answer it like this.

For , it's just like saying and then subbing in in the place of . Since we know is going to be , we use the bottom part of the hybrid function (because we are subbing in -2 so we see which part of the hybrid function defines x when it is < 0.

So I'll just show you a and d, you can try do b and c yourself.

a)



=

Then sub in x = -2

=
=

d)



Since we are looking at subbing in x when it is 2 (which is > 0), we use the bottom part of the hybrid function.



()

Then you can sub in 2.

= ()

= ()
 
=

If you want me to write out how to do the 2nd part of the question step by step, I can do that later, you just have to equate the equations and solve for x, but you have to take into consideration the hybrid function.
I might have made errors there...  someone else can correct me if I've made mistakes.

For the rest of question a) are these, right?



Substituting x=-1






Substituting x=1

[bully3000]

nvm, yep think so!