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Determine (a) $f(x)+g(x),$ (b) $f(x)-g(x),$ (c) $f(x) g(x)$ (d) $f(x) / g(x)$ when defined.$f(x)=3 x-2 \quad g(x)=4 x+7$

(a) $7 x+5$(b) $-x-9$(c) $12 x^{2}+13 x-14$(d) $\frac{3 x-2}{4 x+7} \quad x \neq-\frac{7}{4}$

Algebra

Chapter 1

Functions and their Applications

Section 2

Basic Notions of Functions

Functions

Oregon State University

McMaster 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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01:02

for this problem, we've been given to functions F of X equals three X minus two and G X equals four X plus seven. And we're going to combine these functions in four different ways. We're going to add, subtract, multiply and divide. So let's begin with addition ffx plus G of X. Well, the good thing about we do all these arithmetic operations on functions is that they work pretty much the way you'd expect them to. For addition, I'm going to take F of X, which is three X minus two, and I'm going to add G X, which is four X plus seven. And we could just add are like terms that gives us seven X Plus five is my addition. What about subtraction? F of X minus G of X? We're going to set it up pretty much the same way I get three X minus two minus four X plus seven. The only thing to remember here is that you are subtracting all of G of X. So you do need thio distribute that subtraction. So this is really three X minus two minus four X minus seven and we put those together. We get negative. X minus nine. Okay, now let's try multiplication F of X times G FX. Well, that's going to give me three X minus two times four x plus seven. So we're just gonna have to multiply these by no meals and foil them to get our final answer. So first three x times four x There's 12 x squared, my outer and inner 21 x minus eight x That gives me plus 13 x and I finish with minus 14. And finally we're going to do division. That's gonna be f of X, divided by G F x so f of X goes on top. G of X goes on the bottom. So that's my quotient. Now there is one thing we need to add here that we haven't had to worry about for my other cases I have a denominator on. We need to make sure that our denominator doesn't equal zero because that would give me a number that that just doesn't work. I can't have zero in the denominator, so I can't have four X plus seven equaling zero. And if I solve that for X, I get negative 7/4 so we need to just put the little caveat on here. That X cannot equal negative seven force and that's a really bad seven. Let me try to write that again. Ex cannot equal negative 7/4 it

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