functions

[khalil]

If, for x>5, g(x)= In(x-5) and 2((g(x))=g(f(x)) then f(x) is equal to:
ans: x^2-10x+30, but I got (x-5)^2

[dcc]

Comparing these, we find:

(check domains).  This is the answer that they have given.

[TrueTears]

where



but for remember ran f dom g





Thus we must restrict the domain of f so that ran f dom g

Thus we must move f(x) up 5 units (but remember f(x) = 5 is not included) thus the range becomes which is now a subset.

Thus the equation becomes

EDIT: beaten.

[khalil]

where



but for remember ran f dom g





Thus we must restrict the domain of f so that ran f dom g

Thus we must move f(x) up 5 units (but remember f(x) = 5 is not included) thus the range becomes which is now a subset.

Thus the equation becomes

EDIT: beaten.

How do we know what the range of f(x) is?

[TrueTears]

That's weird why won't the LaTeX show up in my post?

Anyway there's 1 line that is missing after my first line, it doesn't show up in LaTeX

It is X = (x-5)^2

So the range is

[khalil]

Its as easy as 1,2,3

[khalil]

Another

If f: [0,2pie] where f(x)= sin 2x and g:[0,2pie] g(x)=2sinx, then the value of (f+g)(3pie/2) is:

I got -2, answer is 2

[m@tty]

I believe it should be -2

[khalil]

Are you sure?
Its in ch 8 Q6, or if u use a diff type of essentials, its the blue part of the book the first one q)6