Question

evaluate the function as indicated. Determine its domain and range. x^2+2, x<1. 2x^2+2, x>1.
A: f(-2). B: f(0). C: f(1). D: f(s^2+2).

Answer 1

@ash2326 @waterineyes I only need help basically with D.

Answer 2

A,B,C I plugged those values into the first function..since they are either less than or equal to 1!

Answer 3

There are two functions given..

What we have to do first I am not getting...

Second part of your question is clear I am not getting the very first statement..

Answer 4

I have to plug in the values, lets say f(-2) into the appropriate function first.... for a,b,c, and d. lastly, i find their domain and range..

Answer 5

since -2 is less than 1, i would plug that into the first function.. ok?

Answer 6

Yes you are going right..
Go ahead..

by putting x = -2 what you got??

Answer 7

i got 6, for f(-2).. I'm not sure thats right, but i am pretty sure

Answer 8

Have faith on yourself dear..
You are right..

Now do the same by putting x = 0..

Answer 9

Ok. for f(0) i got 2

Answer 10

Yes this one is also correct..

Now find f(1) by putting x = 1..

But be careful do you know where it is to be plugged in?

Answer 11

first one, since it is also equal to.. i got 3

Answer 12

But in the question either < is given or > is given..

I did not see any equal sign there with inequality..

Answer 13

I forgot tp include, sorry. equal sign should be in first function only

Answer 14

with that being said @waterineyes , can u help with D?

Answer 15

@schmidtdancer I'll help you with D

Answer 16

Then you are right..

Answer 17

kk thx guys

Answer 18

s^2+2,
s^2 is always positive so, s^2+2>2 for all s values
so just put x=s^2+2 in the f(x) given for x>1

Answer 19

kk so plug that into the second function

Answer 20

See as you have plugged for x= 1, -2 etc etc now replace x by \(s^2 + 2\)..

Answer 21

Yeah
\[f(s^2+2)=(s^2+2)^2+2\]

Answer 22

Yes you have to plug it in second because \(s^2 + 2 > 0\)..

Answer 23

yay thats what i had!!

Answer 24

Show your work..

Answer 25

shouldn't there be a 2 in front of that @ash2326

Answer 26

like 2(s^2+2)^2 + 2

Answer 27

oh I missed the 2
\[f(s^2+2)=2(s^2+2)^2+2\]

Answer 28

Yes you are right..

Answer 29

im not sure how to simplify the rest

Answer 30

For simplification you can use the formula:

\[(a+b)^2 = a^2 + b^2 + 2ab\]

Answer 31

2s^4+6..thats what I got when I did that but I honestly have no idea

Answer 32

\(a = s^2\) and \(b = 2\) there..

Just use the formula and try to do at least this step only..

Answer 33

s^4+4 +2ab?

Answer 34

Why you did replace a and b in 2ab term??

Answer 35

Sorry did not..

Answer 36

s^4+4+2(s^2)(2)

Answer 37

Yes...

Now put this in that expression..

Answer 38

4s^2+s^4+4

Answer 39

Yes now put it in original expression we have just found..

Answer 40

which is what agin?

Answer 41

\[= 2(s^4 + 4s^2 + 4) + 2\]

can you solve this ??

Answer 42

that is 2s^4+8s^2+4

Answer 43

?

Answer 44

you are confusing me now...

Wait..

Just cool your mind for 30 seconds...

Answer 45

Wait, I thought that was right?

Answer 46

2(s4+4s2+4)+2 <-- this equals what I put

Answer 47

Yes now you got it..
Now solve it and tell me what you get..

Answer 48

I got 2s^4+8s^2+4....

Answer 49

+10 i mean

Answer 50

Yes now are right..

Finally you did that..

Answer 51

So 2s^4+8s^2+10 is the answer

Answer 52

yes this is value of \(f(s^2 + 2)\)..