Question

Please help :)
Express the following function, F(x), as a composition of two functions, f and g. f(g(x)).
F(x)= (sqrt3x-4)
Part 1: Find g(x) by identifying the function you are taking the square root of.

Part 2: Find f(x) by identifying what you are doing to the function you found in part 1. What function is f(X)?

Part 3: Verify that f(g(x))=f(x)
f(g(x))=(sqrt3x-4)

Answer 1

ok do you know what composition is?

Answer 2

yep! but i'm a little confused especially on verification

Answer 3

suppose we have the function \(f(x) = \sqrt{x}\)

Then \(f(4) = \sqrt{4}=2\) and \(f(25) = \sqrt{25} = 5\) and \(f(3) = \sqrt{3}\) and

\(f(2x)=\sqrt{2x}\)

Answer 4

what do we need \(g(x) \) to be so that we have \(f(g(x)) = \sqrt{3x-4}\)?

Answer 5

sqrtx?

Answer 6

we are letting \(f(x) = \sqrt{x}\).

Answer 7

hint:

\(f(\color{blue}{g(x)})= \sqrt{\color{blue}{3x-4}}\)

Answer 8

what is \(g(x) = \)?

Answer 9

oh! √x ?

Answer 10

no

Answer 11

you are just saying the same thing over and over...

Answer 12

wait sorry

Answer 13

i wasn't paying attention

Answer 14

right

Answer 15

3x-4

Answer 16

correct

Answer 17

ok, so do you see why we choose \(f(x) = \sqrt{x}\)?

Answer 18

yeah i get that now haha

Answer 19

the last part makes no sense. It is not true that \(f(g(x))= f(x)\)

Answer 20

it then says f(gx)) = (sqrt3x-4) though so is it still totally wrong