Help quick

Mathematics

2 answers:

Naya [18.7K]3 years ago

6 0

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 $y$ coordinate, the solution of $f(x)=g(x)$ will be the $x$ 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 $g(x)=-x+7$ , so $f(x)=g(x)$ is equivalent to $2x+1=-x+7$ . The only thing left is solving the equation for x:
$2x+1=-x+7$
$3x=6$
$x=2$
As you can see, both ways gives us the same answer: the solution to the equation $f(x)=g(x)$ is $x=2$ .

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 $x$ 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 $x$ :
$x+2=2x+1$
$x=1$
And just like before, both ways gives us the same answer: the solution to the equation $f(x)=g(x)$ is $x=1$

So, the answer that you should enter in your boxes are: 2 in the first, and 1 in the second one.