Question

What is the value of f[g(5)] for the functions f(x) = 2x + 1 and g(x) = 2x - 5? (Type only the value of your final answer, no variables.)

Answer 1

f[g(5)] is a 2-step process. You work from the inside in. So first off you have to find g(5). Can you do that?

Answer 2

not really :( if you can teach this stuff to me thatd be great

Answer 3

Absolutely!

Answer 4

So when I say g(5), we're referring to g as a “function”. Above, the function is defined as:

g(x) = 2x - 5

That means that, given a number x, to get the value of g(x), you multiply that number by 2 and then subtract 5.

Answer 5

IS it always by 5 that you subtract?

Answer 6

No, that's just how g(x) is defined in this particular case.

Answer 7

So it would be 2x5-5

Answer 8

So for g(x) the way it's pointed out above, we would have:

\[\begin{align}
g(1) &= 2\cdot 1- 5 &= 2 - 5 &= -3\\
g(2) &= 2\cdot 2- 5 &= 4 - 5 &= -1\\
g(3) &= 2\cdot 3- 5 &= 6 - 5 &= 1\\
g(4) &= 2\cdot 4- 5 &= 8 - 5 &= 3
\end{align}\]

Answer 9

Yep, g(5) would be exactly that! Which gives us?

Answer 10

5 again

Answer 11

Exactly :)

Answer 12

So now we know that g(5) = 5.

But we're looking for f[g(5)]. Once we know g(5) = 5, we can put it in wherever g(5) shows up. In this case:

f[g(5)] = f(5)

Answer 13

Now we can plug 5 into the definition of f(x). Can you do that?

Answer 14

f(5) like you already did wouldnt it be?

Answer 15

Not quite, f(x) is 2x + 1. So we plug 5 into that equation now.

Answer 16

2*5+1

Answer 17

=11

Answer 18

Exactly! :)

Answer 19

So f[g(5)] = f(5) = 11

Answer 20

now what xD

Answer 21

hello ?

Answer 22

Sorry! Haha. That's it? That's the answer to the question :)

Answer 23

o ok thank you lol thought there was more to it

Answer 24

Nope :) Not that I can see, anyway.