1. ## Functions

Given that $f(x)=3x^2-3\ \mbox{and}\ g(x)=\sqrt{x-2}$

evaluate

$fg (x)$

I am a bit confused on how to multiply these two functions.
Am I allowed to times each of the terms under the square root sign separately(probably not)?

How do I perform this operation then?

Thank you!

2. Its probably asking for the composition of $f$ and $g$. $fg(x)$ is another way of writing $f \circ g$ or $f(g(x))$.

So $f \circ g = 3(\sqrt{x-2})^2 - 3 = 3x-9$.

3. Thank you!

I don't really know if this is asking for composite functions(since we still have not gone through them), but our teacher told us to substitute the function of f(x) in the place of f and then times the two functions.

For example

if we had $(f+x) (6)$ then it would have been $3x^2-3+\sqrt{x-2}$substituing 6 in place of x.

4. Originally Posted by Coach
Thank you!

I don't really know if this is asking for composite functions(since we still have not gone through them), but our teacher told us to substitute the function of f(x) in the place of f and then times the two functions.

For example

if we had $(f+x) (6)$ then it would have been $3x^2-3+\sqrt{x-2}$substituing 6 in place of x.
that notation makes no sense. i think you meant f(x + 6), in which case, that would be $3(x + 6)^2 - 3$ ........and you would simplify that

5. Ok.

I think you may be right, but that is exactly what my homework says.

6. Originally Posted by Coach
Ok.

I think you may be right, but that is exactly what my homework says.
it's probably a typo then.

7. Originally Posted by Coach

Given that $f(x)=3x^2-3\ \mbox{and}\ g(x)=\sqrt{x-2}$

evaluate

$fg (x)$

I am a bit confused on how to multiply these two functions.
Am I allowed to times each of the terms under the square root sign separately(probably not)?

How do I perform this operation then?

Thank you!
Originally Posted by tukeywilliams
Its probably asking for the composition of $f$ and $g$. $fg(x)$ is another way of writing $f \circ g$ or $f(g(x))$.

So $f \circ g = 3(\sqrt{x-2})^2 - 3 = 3x-9$.
tukeywilliams is probably right, but if you see the notation
(fg)(x)
it means simply to multiply f(x) and g(x).

Similarly:
(f/g)(x) = f(x)/g(x)
(f + g)(x) = f(x) + g(x)
(f - g)(x) = f(x) - g(x)

-Dan