For a given function f(x) we define the domain restrictions as values of x that we can not use in our function. Also, for a function f(x) we define the inverse g(x) as a function such that:
g(f(x)) = x = f(g(x))
<u>The restriction is:</u>
x ≠ 4
<u>The inverse is:</u>
Here our function is:
We know that we can not divide by zero, so the only restriction in this function will be the one that makes the denominator equal to zero.
(x - 4)^2 = 0
x - 4 = 0
x = 4
So the only value of x that we need to remove from the domain is x = 4.
To find the inverse we try with the general form:
Evaluating this in our function we get:
Remember that the thing above must be equal to x, so we get:
From the two above equations we find:
b = 11
a = 4
Thus the inverse equation is:
If you want to learn more, you can read:
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Answer:
the second box for y is 9
the third box for x is 2.5
im not sure about the third box for y
Answer: y = 1/2 or y = -1/2
Step-by-step explanation:
First move the 1 to the side with the 0
-4y^2 = -1 // -1 because when you move a number to the other side of the equation you have to multiply -1
Then divide by -4 on each side
y^2 = 1/4
square root each side
|y| = 1/2 // sq rt y^2 becomes an absolute value because when you square root a square it automatically becomes an absolute value
so the answer would be y = 1/2 or -1/2
to check just put it into the equation as y. Both work.
Answer:
a
Step-by-step explanation:
sec (thita) = squrt (5)
squaring on both sides:
sec^2 (thita) = 5 - equation 1
1 + tan^2 (thita) = 5
tan^2 (thita) = 4
tan (thita) = 2.
= tan (thita) - squrt(5)sin(thita)
= 2 - squrt(5) x 2/ squrt(5)
= 0
from eqn - 1
sec(thita) = squrt(5)
cos(thita) = 1/ squrt(5)
sin(thita) = squrt ( 1- 1/(squrt (5))^2)
sin(thita) = 2/ squrt(5) .
