Find two functions f and g such that h(x)= [f o g](x). Neither function may be the identity function f(x)=x.

Question

h(x)= (square root) √(2x-6-1)

h(x)=

Please walk through the steps to solve this as well as the solution

Answer 1

Hi,

I dont think h(x) = √(2x-6-1) is right

it doesn't make sense.

but h(x)= fog(x) = f(g(x)) = √(2x-6-1) I

and we know f(x) = x ------> plug in g(x) in this equation!

f(g(x)) =g(x) II

by compare I and II you figure out left side are the same, so must be right side also will be the same, as a result g(x) = √(2x-6-1) dont care what h(x) is.

Important note : when you need to find fog when f(x) = x always the result is: fog = g :)

I hope it is useful, please let me know if you have any question.

Minoo