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Given the function defined by the equation $g(x)=2 x \sqrt{x+1}$ determine (a) $g(0),$ (b) $g(-1),$ (c) $g(3),$ (d) $g(8),$ (e) $g(2 x)$

(a) 0(b) 0(c) 12(d) 48(e) $4 x \sqrt{2 x+1}$

Algebra

Chapter 1

Functions and their Applications

Section 2

Basic Notions of Functions

Functions

Oregon State University

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

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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03:11

01:51

02:58

for this problem, we have been given a function g of X equals two x times the square root of X plus one. And for this problem, we're going to take this function and we're going to evaluate it at a variety of different points to start with. Let's find G of zero. Well, what do we mean by G of zero G F zero means I'm going to go find my G function, which is a function we've been given and everywhere where there's an X in my function. I'm going to substitute what's inside my parentheses in this case zero. So for G F zero that's gonna become two times zero times the square root of zero plus one. So every X is now replaced with zero. Well, this is going to just give me zero, because I have a factor of zero in my answer. Okay, let's try another one. Let's try G of negative one again. I go to my GI function everywhere, everywhere there's an X, I'm going to substitute and negative one. So that gives me two times negative one times the square root of negative one plus one. Well, under that radical, I'm gonna have zero so negative two times zero again is just zero. Let's try a third number G of three g function. I'm going to substitute in three for every X. Well, that's square roots. A square to four. That's too. Two times three times to gives me 12. Hey, one more number g of eight. Oh, looking back at my original function, that's two times eight plus the square root of eight plus one. The square root of nine is gonna be 32 times eight times three is going to be 48. Okay, now we've just been substituting in numbers. We can also substitute in an expression, something that maybe has a variable in it. For example, g of two x. Well, just because there's a variable, it doesn't change the process. We're still going to go to the G function. And everywhere that we have an X in our original function, we're going to substitute in what's inside our parentheses in this case two x So what I have is to times two x There's my first substitution times. The square root of two x substituted again, plus one. And if I multiply this out, I have a four X in the front times the square root of two X plus one. The answer isn't this nice and neat is the other ones. I don't have to just a play number, but that's okay. Typically, if I input in a variable, I'm gonna end up with a variable. Uh, in my answer. So for this function, G, you can see how is evaluated two different results using some different inputs for X.

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