Question

let f(x)=log(x^2-2x) and g(x)=x/x-1. which expression represents (fog)(x)? a)log(x^3-2x^2/x-1) b)xlog(x^2-2x)/x-1 c)log(x^2-2x)/log(x^2-2x)-1 d)log(x^2-2x(x-1/(x-1)^2)

Answer 1

Problem: let f(x)=log(x^2-2x) and g(x)=x/x-1. which expression represents (fog)(x)?

Solution:

notice that:

`(f\circ g)(x)\text{ = f(g(x))}`

then, the composition would be:

`(f\circ g)(x)\text{ = f(g(x)) = log( (}(x)/(x-1))^2-2\text{(}(x)/(x-1))\text{ )}`

this is equivalent to

`=\text{ log( }(x^2)/((x-1)^2)^{}-(2x)/(x-1)\text{)}`

this is equivalent to (Making common factor):

`=\text{ log( }(x^2-2x(x-1))/((x-1)^2))`

then the correct answer would be:

`=\text{ log( }(x^2-2x(x-1))/((x-1)^2))`