Let f(x) = log(x^2-2x)and g(x)=x/x-1.
Which expression represent (f o g) (x)?

i # 2

Step-by-step explanation:

Hi!

to understand this problem it is important to know that f(g(x)) means that every x in the f(x) expression is replaced by the expression of g(x)

f(x) = x2- 2x    and  g(x)= √(1-x)

f(g(x)) = ( √(1-x) )2   -  2(√(1-x) )

0 =  1-x  - (2 (√(1-x) )

subtract 1-x from both sides

x-1 = - (2 (√(1-x) )

Divide -2 by both sides

 ( (x-1) /  -2 )  = √(1-x)

To remove square root take the square of both sides

( (x-1) / -2 )2 = 1-x

(x-1)2 / (-2)2 = 1-x

(x-1) (x-1)     /  (-2)2      =   1-x  

(x2 - 2x + 1) / 4   =    1-x

Multiply by 4 on both sides

(x2 - 2x + 1) = 4 - 4x

x2 + 2x - 3 = 0

Factor

(x-1)(x+3) =0

zeros = 1 and -3

x intercepts (1,0) and (-3,0)

the domain will be x≤1 or (-∞,1)

domain shortcut: if you graph this function (desmos works great) it is easy to find the domain

Step-by-step explanation:

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so far i think you have the right thing going for you just remember soh cah toh

step-by-step explanation:

sine over hypotenuse

cosine   equals adjacent

tangent over hypotenuse