Mathematics, 04.08.2019 07:40 Asrys

Quick 1. graph f(x)=2x+1 and g(x)=−x+7 on the same coordinate plane. what is the solution to the equation f(x)=g(x) ? 2. let f(x)=x+2f(x)=x+2 and g(x)=2x+1 . graph the functions on the same coordinate plane. what are the solutions to the equation f(x)=g(x) ? enter your answers in the boxes. x = or x =

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Answer from: doll1234

1.You have two ways for solving this.
First, you could use a graphing utility or calculator to graph both functions on the same plane, and given that the functions do not have a

coordinate, the solution of f(x)=g(x)

will be the

coordinate in which the tow graphs intercept (cross each other) as you can see in the picture (1).
The other way is equating the two equations and solve for x:
We know that f(x)=2x+1

and

, so

is equivalent to 2x+1=-x+7

. The only thing left is solving the equation for x:
2x+1=-x+7

As you can see, both ways gives us the same the solution to the equation f(x)=g(x)

.

2. For this one we can repeat the exact same procedures as before:
Graph the functions on the same plane using a graph calculator or graphing utility, and identify the

coordinate in which the two graphs intercept as you can see in the picture (2), or you we can also equate both equations, and solve for

And just like before, both ways gives us the same the solution to the equation f(x)=g(x)

So, the answer that you should enter in your boxes are: 2 in the first, and 1 in the second one.
Quick 1. graph f(x)=2x+1 and g(x)=−x+7 on the same coordinate plane. what is the solution to the equ

Quick 1. graph f(x)=2x+1 and g(x)=−x+7 on the same coordinate plane. what is the solution to the equ

Answer from: Quest

2.) is the most sense

Answer from: Quest

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

=3x+1

=3(2)+1

since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

=x+1

=2+1

now, let's find g(2)g(2):

g(x)

g(2)

=2x

=2⋅2

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

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