<h2>
Step-by-step explanation:</h2>
A: f(x)=8x-2
1. Switch the f(x) to y
y=8x-2
2. Switch y to x and x to y
x=8y-2
3. Solve for y:
------------------------------
1. Add 2 to both sides.
x=8y-2
+2 +2
2. Divide both sides by 8.
x+2=8y
--- ---
8 8
1/8x+1/4=y
3. Write in f-inverse form
f^-1(x)=1/8x+1/4
B: g(x)=2/3x+6
1. Switch the g(x) to y
y=2/3x+6
2. Switch y to x and x to y
x=2/3y+6
3. Solve for y:
------------------------------
1. Subtract 6 from both sides.
x=2/3y+6
-6 -6
2. Multiply both sides by 3/2 (to cancel out the 2/3)
x-6=2/3y
2/3x-4=y
3. Write in f-inverse form
g^1(x)=2/3x-4
C: h(x)-4x-12
1. Switch the h(x) to y
y=-4x-12
2. Switch y to x and x to y
x=-4y-12
3. Solve for y:
------------------------------
1. Add 12 to both sides.
x=-4y-12
+12 +12
2. Divide both sides by -4
x+12=-4y
------ ---
-4 -4
-1/4x-3=y
3. Write in h-inverse form
h^2(x)=-1/4/x-3
Answer:
(d) x = -3/4; y = -3 1/2
Step-by-step explanation:
You are asked for the coordinates of the point of intersection of the lines on the graph. This requires interpolation, because not all grid lines are marked, and the point is not on any grid line.
<h3>Interpolation</h3>
The idea of "interpolation" is figuring the value of a point that lies between points whose values are known. The answer choices here suggest that we are to interpolate to the nearest 1/4 unit. This requires that you mentally (or actually) divide the space between grid lines into 4 equal sections, and figure where the point lies relative to those divisions.
In the case of the x-coordinate, the first grid line left of the y-axis is not marked, but we notice it lies halfway between x=0 and x=-2. That means we can safely assume that the unmarked vertical grid line has a value of x=-1.
<h3>Application</h3>
<u>horizontal coordinate</u>
The location of the point of intersection of the two lines is horizontally closer to the -1 (unmarked) grid line than it is to the y-axis. Its x-value will be between -1 and 0. The answer choices tell us it is -3/4, consistent with it being about 3/4 of the distance toward -1 from 0.
x = -3/4
<u>vertical coordinate</u>
The location of the point of intersection of the two lines is vertically about halfway between -3 and -4. The answer choices tell us it is -3 1/2.
y = -3 1/2
The answer is 45 because 2.50 times 18=45
Answer:
X=4
Step-by-step explanation:
7x+4y=28
7x+4(0)=28
7x=28
X=4
Answer:
5
Step-by-step explanation:
The value of "b" is the y-intercept. The point is (3,5). 5 is the y intercept so bb is equal to 5.
