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Given the function defined by the equation $f(x)=\frac{x+1}{2 x-3}$ determine (a) $f(0),(\text { b) } f(-1),(\text { c) } f(3),(\text { d) } f(2 x),(\text { e }) f(x+h)$

(a) $-1 / 3$(b) 0$(c) 4 / 3$(d) $(2 x+1) /(4 x-3)$(e) $(x+h+1) /(2 x+2 h-3)$

Algebra

Chapter 1

Functions and their Applications

Section 2

Basic Notions of Functions

Functions

Missouri State University

Oregon State University

Harvey Mudd College

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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03:03

Given the function defined…

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02:27

Given $f(x)=x^{2}+2 x+3,$ …

07:26

Find the following for eac…

0:00

Find the function values.<…

02:21

For each function find:

01:31

Given $f(x)=2 x^{2}-3 x,$ …

01:49

01:50

Determine whether the equa…

12:39

04:12

00:23

Given the one-to-one funct…

for this problem. We've been given a function f of X equals X plus one divided by two X minus three. And our goal for this exercise is to, uh, find the value of this function at some given input points. So let's begin. Let's start with F of zero. What does it mean when we cf zero? What it means is we're going to go find our F function, which is our function we've been given and everywhere where an X appears in that function. I'm going to substitute in the value of my parentheses in this case, zero. So if I go to the F function, I'm gonna put in a zero every time I see an X in my function. So if I evaluate this and simplify it, I end up with negative one third. Okay, let's try a different number. Let's do f of negative one again. Go to the F function and substitute negative one end. Now, when I see X, that'll be negative. One plus one over two times. Negative one minus three. Well, the top of that is going to be zero. The bottom is gonna be negative. Five, which means that simplifies to zero. Okay, One more number. Let's put in f of three function F Substitute three and for X. That gives me three plus one over two times three minus three. So my numerator is for and my denominator is three. So f of three is four thirds. Now we've been substituting numbers in for X. You can also substitute expressions things that maybe have variables in it. For example, f of two X. Well, just because there's a variable in those parentheses, the process doesn't change. I'm still going to the F function and where I see X in the original, I'm going to substitute two X so that's going to give me two X plus one over two times two X minus three. And let's get rid of those parentheses That gives me two X plus one over four X minus three. Now, this isn't as nice of an answer. Doesn't look as nice as the numbers. I still have a letter in it, but that's okay, because I input it a variable into my function. Typically, if I input in a variable, I'm gonna have a variable in my output. So they put two X that fractions what we get out. Let's try one more of thes. Let's do F of X plus H well original function Everywhere. There's an X now gets an X plus h, so I have X plus H plus one over two times X plus H minus three. And again, let's get rid of our parentheses. That gives me a denominator of two x plus two H minus three. So for our given function F, here are the results when we evaluate our function at various different values for X.

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