Question

Let f(x) = x-2/4 and g(x)= 2x^2+4.
a. Find f(g(x)).
b. Find g(f(x)).

Answer 1

Do you know how to calculate f(1), for example, using f(x) you are given?

Answer 2

No I have no clue where I start or what I am supposed to do. I am looking through my book right now to try to find an example.

Answer 3

If you have a function, such as f(x) = 2x. Do you know how to do f(1)?

Answer 4

No, I have no clue where I start or what I am supposed to do.

Answer 5

f(g(x))= f(2x^2+4)= ???
g(f(X))= g(x-2/4)= ???

Answer 6

Ok. Let's do it step by step.
Let's say you have a function that is
f(x) = 2x
That means the same as y = 2x
If you are asked to find f(1), all you need to do is substitute 1 in for x and calculate:
f(x) = 2x
Evaluate f(1).
f(1) = 2(1) = 2, so
f(1) = 2

Answer 7

okay I understand that

Answer 8

If you are asked to find f(t), then you replace x with t.
Since in my example, f(x) = 2x, f(t) = 2t

Answer 9

Now let's look at your problem.
You have 2 given functions. One is called f and one is called g.
Function f is defined as f(x) = (x - 2)/4, and fungtion g is defined as g(x) = 2x^2 + 4

Answer 10

Look carefully at function f, f(x) = (x - 2)/4
If I were to ask you to find f(5), you would replace x with 5 and calculate.
For you problem's f(x) = (x - 2)/4, f(5) is:
f(5) = (5 - 2)/2 = 3/2

Answer 11

f(g(x)) = f(2x^2+4) = x-2/4(2x^2+4) = ???
g(f(X)) = g(x-2/4) = 2x^2+4(x-2/4) = ???

Answer 12

What your problem is asking is to find the value of f(x) evaluated at g(x). That is what
f(g(x)) means. Instead of putting a number in for x, like putting 5 in for x to calculate
f(5), they want you to put g(x) in for x.

Answer 13

f(g(x)) = f(2x^2 + 4) = (2x^2 + 4 - 2)/4 = (2x^2 + 2)/4 = 2(x^2 + 1)/4 =(x^2 + 1)/2