F(x) = -3x – 1 g(x) = x2 + 6x – 12 Find: g(f(x))
1 answer:
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There are 3 ways you could solve this
1. You could graph it.
2. You could equate the line to the quadratic
3. You could just put the x value of the points into both equations until you get the same y value. It sometimes is the only way to solve a multiple choice math question. I do the first two ways.
Step One
Graph the two equations.
The graph is below.
Step 2
From the graph determine the answers.
There are two points where the graphs coincide
Check out D
Step 3
Equate the two equations. The y values must be the same.
6x + 6 = -x^2 + 5x + 6
Step 4
Solve
6x + 6 = - x^2 + 5x + 6 The 6s cancel which is very handy.
6x = -x^2 + 5x Pull the 2 terms on the left over to the right.
6x - 5x = -x^2
x = - x^2
x^2 + x = -x^2 + x^2
x^2 + x = 0 Factor
x(x + 1) = 0
That means that
x = 0
or
x + 1 = 0
x = - 1
Step 3
Find the ys
y = 6x + 6
if x = -1
y = 6(-1) + 6
y = -6 + 6
y = 0
One of the answers is
(-1,0) <<<<<<<< Answer
Now for the other one
y = 6x + 6
x = 0
y = 6(0) + 6
y = 6
The other point is (0,6) answer <<<<<<<
D <<<<<< Total answer
There are 3 ways you could solve this
1. You could graph it.
2. You could equate the line to the quadratic
3. You could just put the x value of the points into both equations until you get the same y value. It sometimes is the only way to solve a multiple choice math question. I do the first two ways.
Step One
Graph the two equations.
The graph is below.
Step 2
From the graph determine the answers.
There are two points where the graphs coincide
Check out D
Step 3
Equate the two equations. The y values must be the same.
6x + 6 = -x^2 + 5x + 6
Step 4
Solve
6x + 6 = - x^2 + 5x + 6 The 6s cancel which is very handy.
6x = -x^2 + 5x Pull the 2 terms on the left over to the right.
6x - 5x = -x^2
x = - x^2
x^2 + x = -x^2 + x^2
x^2 + x = 0 Factor
x(x + 1) = 0
That means that
x = 0
or
x + 1 = 0
x = - 1
Step 3
Find the ys
y = 6x + 6
if x = -1
y = 6(-1) + 6
y = -6 + 6
y = 0
One of the answers is
(-1,0) <<<<<<<< Answer
Now for the other one
y = 6x + 6
x = 0
y = 6(0) + 6
y = 6
The other point is (0,6) answer <<<<<<<
D <<<<<< Total answer