Solving Functions

Question

The function  can be expressed in the form  where  and  is 

Answer 1

h(x)= x-8

= -(x-8)

h (x) =-g (x)

h (x)=f(g (x)) means expressing h in terms of g.

in other words, how is g transformedinto h.

So, that function that transforms g in h is f= -x

Answer 2

Since g(x) = x-8, we can rewrite f(g(x)) as f(x-8). Also, 1x is the same as just x, so 1x-8 is the same as just x-8.

So now we have f(x-8) = x-8. So f(x) doesn't really do anything; it just spits out whatever you put in the parentheses. Therefore f(x) = x. Fyi, this is called the identity function.

I hope that was clear. Have a great day Patricia!