Math Is Fun Forum

denis_gylaev

Member

Registered: 2015-03-19

Posts: 66

Functions Help

Part 1:

Let f(x) = 3x^2 - 4x. Find the constant k such that f(x) = f(k - x) for all real numbers x.

Part 2:

Consider the functions
\[f(x) = \sqrt{\dfrac{x+1}{x-1}}\qquad\qquad\text{and}\qquad\qquad g(x) = \dfrac{\sqrt{x+1}}{\sqrt{x-1}}.\]
Explain why f and g are not the same function.

Last edited by denis_gylaev (2015-04-12 05:17:24)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Functions Help

hi denis_gylaev

Q1.  replace x by k-x to get

Simplify and set the x coefficients equal and the constant terms equal, to get k.

Q2.  There's a lot of code here that doesn't display with this forum's Latex.  At least, not for me.  Did it for you?

Here's what I think you meant:

f can take any values except between 0 and -1.  g can only take values above 1.

Check out at http://www.mathsisfun.com/data/function-grapher.php

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Functions Help

Hi Bob

I don't think f can take values between 0 and 1 either.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Functions Help

hi Stefy, 

In my head I said that too. Just forgot to put it down.  Thanks.  On the graphs it is obvious.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob