Question

If f(x)=x^2 + 2, find and simplify the following...

f(t+1)=______
^^ would it be like this? f(t+1)=(t+1)^2 + 2 ?
if so, would it need to be simplified more?

f(t^2 + 1) = ______
^^would it be like this? f(t^2 + 1)=((t^2 + 1)^2+1)
again, would it need to be simplified more?

f(2)=_____
^^would it be f(2)=2^2 + 2 = 4+2=6 ??

2f(t)=____
^^not too sure on this one.... would it start off like this? 2(t^2+2)=2t^2 + 4 ?? is that right? :/

(f(t))^2 + 1 =_______
^^not very sure on this one.. :(

Please explain? Thanks!!! :)

Answer 1

^yeah in that case, usually simplifying is better.

Answer 2

ohh okay... so for the first one it just becomes t^2 + 1 +2 = t^2 + 3 ?

Answer 3

You overcomplicated this one: 2f(t).

Find f(t) first, that's easy.

Then multiply it by 2.

Answer 4

ohh okay... so 2f(t)=(t^2+2)2 = 2t^2 + 4 ?? is that right?

Answer 5

Oh you kinda did that, just your explanation was weird. Yes.

Answer 6

haha ohh oops sorry about that :P

Answer 7

(f(t))^2 + 1

Square f(t), and then add 1

Answer 8

(t^2+2)^2= t^4 + 4 ?

then add 1, and would you get t^4 + 5 ?

is that correct? :/

Answer 9

^nope. You can not do that.

(a+b)^2 does NOT equal a^2 + b^2

How do you square a number? Multiply it by itself. Do that with (t^2+2)^2

Answer 10

aw darn...

so 2t^2 + 4 ? :/

Answer 11

a^2 = a*a

(a+b)^2 = (a+b)(a+b)

Answer 12

ohh i see now

so (t^2+2)(t^2+2)= t^4 + 4t^2 + 4 ??

Answer 13

Now find (f(t))^2 + 1

Answer 14

t^4 + 4t^2 + 5 ?

Answer 15

if so, are these the correct answers?

f(t+1)= t^2 + 2t + 4

f(t^2+1) = t^4 + 2t^2 + 3

f(2) = 6

2f(t) = 2t^2 + 4

(f(t))^2 + 1 = t^2 + 2t + 4

are those all correct?

i fixed the first two and did it the way you said using FOIL... :/

Answer 16

(f(t))^2 + 1 = t^2 + 2t + 4 you have this wrong now, had the right answer above.

Answer 17

oh oops sorry i meant + 5 haha

(f(t))^2 + 1 = t^2 + 2t + 5

so when it's 5, are the all correct now? :)

Answer 18

Probably, yes.

Answer 19

okay awesome!! :) yay :) thanks so much!!! :D