9514 1404 393
Answer:
g^-1(x) = (7x+1)/(6 -4x)
Step-by-step explanation:
Substitute y for x and solve for y.
g(y) = x
(6y -1)/(4y +7) = x
6y -1 = x(4y +7) . . . . multiply by 4y+7
6y -4xy = 7x +1 . . . . add 1-4xy
y(6 -4x) = 7x +1 . . . . factor out y
y = (7x +1)/(6 -4x) . . . divide by the coefficient of x
Scale factor is the ratio of two corresponding sides.
Here we have two triangles, where the preimage is the smaller triangle and the image is the larger triangle.
So scale factor =14/18 = 7/9
And to find the missing variable, we need to set the ratio.
7/9 = 28/x
Cross multiplying both sides
7x = 28*9
x = 36
8.1 Function of Two Variables
Many functions have several variables.
Ex. There are 3 types of football tickets. Type A costs $50, type B costs $30, and type C costs
$20. If in a match, x tickets of type A, y tickets of type B, and z tickets of type C are sold,
the total income of ticket sale is f(x, y, z) = 50x + 30y + 20z.
Def. A real-valued function of two variables f consists of
1. A domain A consisting of ordered pairs of some real numbers (x, y).
2. A rule that associates with each ordered pair in A with one real number, denoted by
z = f(x, y).
Ex. (Ex 1, p.532) f(x, y) = x + xy + y
w + 2. Compute f(0, 0), f(1, 2), and f(2, 1).
Ex. Find the domain of a. f(x, y) = x
2+y
2
, b. g(x, y) = 2
x−y
, c. h(x, y) = p
1 − x
2 − y
2.
Ex. Find the domain of g(r, s) = √
rs.
The graph of a function z = f(x, y) is the collection of all points {(x, y, f(x, y)) : x, y ∈ A}
in R
3
(Fig 5, p.534; Fig 6, p.535).
The graph of z = f(x, y) is 3 dimensional and it is difficult to draw. So we use level curves.
A level curve is the graph of
c = f(x, y)
on xy-plane for a constant c. By drawing the level curves corresponding to several admissible
values of c, we obtain a contour map. (Fig 7, p.535; Fig 8, p.536)
Ex. Ex 5, p.536.
HW. C8.1: SC1, 2, 3, Ex 31, 33
That's a cubic graph. Anything with that sideways 's' shape is a cubic graph.
207,689= 208,000
Hoped I helped:D
