We have to find the values of F.
In this case. F is unlikely to be a polynomial.
But the problem is, we can’t calculate the values of F directly.
There is no real value of x for which x = x−1 x because F isn’t defined at 0 or 1. so,
substituting x = 2.
F(2) + F(1/2) = 3.
Substitute, x = 1/2
F(1/2) + F(−1) = −1/2.
We still are not getting the required value,
therefore,
Substitute x = −1
As, F(2) +F(−1) = 0.
now we have three equations in three unknowns, which we can solve.
It turns out that:
F(2) = 3/4
F(3) = 17/12
F(4) = 47/24
and
F(5) = 99/40
Setting
g(x) = 1 − 1/x
and using
2 → 1/2
to denote
g(2) = 1/2
we see that :
x → 1 - 1/x → 1/(1-x) →xso that:
g(g(g(x))) = x.
Therefore, whatever x 6= 0, 1 we start with, we will always get three equations in the three “unknowns” F(x), F(g(x)) and F(g(g(x))).
Now solve these equations to get a formula for F(x)
As,
h(x) = (1+x)/(1−x)which satisfies
h(h(h(h(x)))) = xNow, mapping x to h(x) corresponds to rotating the circle by ninety degrees.
Answer:
284.6 square yards
284.6 yd^2
Step-by-step explanation:
Base: 7 × 13 = 91
Rectangle Sides: 6.1 × 13 = 79.3 (x2 = 158.6)
Triangle Sides: 5 × 7 = 35 (÷2 ×2 = 35)
Add: 91 + 158.6 + 35 = 284.6
Answer:
6
Step-by-step explanation:
(x + 9) * (x - 2) = 60
x^2 - 2x + 9x - 18 = 60
x^2 + 7x - 18 = 60
x^2 + 7x = 78
FACTORING:
x(x + 7) = 78
x = 6
Smallest number of cakes that each would have decorated is 18.