Question

The following function may be viewed as a composition h(x)=f(g(x)).
Find f(x) and g(x).

h(x) = sqrt(x^2) - 4 x + 3.

Answer 1

they want me to find f(x) and g(x)

Answer 2

i think i need to use the the product rule?

Answer 3

Is everything inside the square root?
\[ h(x)= \sqrt{x^2-4x+3} \] ?

Answer 4

yes

Answer 5

f(x)=sqrt(x)
g(x)=x^2-4x+3

Answer 6

h(x)= f(g(x))

so if f(x)= sqrt(x)
and g(x)= x^2-4x+3

you would "compose" them, by replacing g(x) in f(g(x)) with the definition
g(x)= x^2-4x+3

so h(x)= f(x^2-4x+3)
that means replace x in f(x)= sqrt(x) with the entire expression x^2-4x+3
to get
h(x) = sqrt(x^2-4x+3)

Answer 7

btw, you should have written instead of h(x) = sqrt(x^2) - 4 x + 3.
h(x) = sqrt(x^2 - 4 x + 3) (with the parens around the whole expression.

sqrt(x^2) - 4 x + 3 really means x - 4x+3 = -3x+3 (sqrt(x^2) is x))

Answer 8

ok so f(X) is is the sqrt of x^2-4x+3?

Answer 9

no \[f(g(x))=\sqrt{x^2-4x+3}\]

Answer 10

then what is f(x)?

Answer 11

\[f(x)=\sqrt{x}\]

Answer 12

the way u guys found g(X) is that reverse product rule?

Answer 13

just x or x^2-4x+3?

Answer 14

This is function composition. Can you explain what you mean by the product rule?

Answer 15

oh i mean the chain rule

Answer 16

Do you mean
h(x) = f(x)*g(x) (where * means multiply)?
If so, no, you do not use the product rule. You use the "composition rule"

Answer 17

the formula is d/d= f(g(x))= f'(g(x))g'(x)

Answer 18

d/dx

Answer 19

i havent learned the composition rule yet

Answer 20

really though just want to find out how to write out f(x) =

Answer 21

Say you have 2 functions:
f(x)=sqrt(x)
g(x)=x^2-4x+3

To compose them to create a new function h(x)= f(g(x))
instead of plugging in a number for x you plug in a function.

so f(g(x)) means replace x in f(x) definition with g(x):
h(x) = f(g(x)) = sqrt( g(x) )
now replace g(x) with its definition
sqrt(g(x) ) = sqrt ( x^2-4x+3)

does that make sense?

Answer 22

ok thanx

Answer 23

it does makes sense