The answer is:
The inverse of a function is another function,
, with the following property:
In other words, the inverse of a function does exactly "the opposite" of what the original function does, and so if you compute them both in sequence you return to the starting point.
Think for example to a function that doubles the input, , and one that halves it:
. Their composition is clearly the identity function
, since you consider "twice the half of something", or "half the double of something".
In general, to invert a function , you have to solve the expression for
, writing an expression like
. If you manage to do so, then
is the inverse of
.
In your case, you have
Multiply both sides by to get
Square both sides to get
Finally, subtract 3 from both sides to get
Since the name of the variables doesn't really have a meaning, you can say that the inverse function is
As for the domain of the inverse function, remember what we said ad the beginning: if the original function goes from set A (domain) to set B (codomain), then the inverse function goes from set B (domain) to set A (codomain). This means that the inverse function is defined on an element in B if and only if that element belongs to the range of the original function, i.e. the set of the elements of the codomain such that there exists
. So, we need the range of
.
We know that the range of is
. When you transform it to
you simply translate the graph horizontally, so the range doesn't change. But when you multiply the function times
you affect both extrema of the range, turning it into
, which you can simply write as
-1(x+2)=2(3x-6) Please solve
First, simplify 1 × (x + 2) to (x + 2) / Your problem should look like:
Second, expand. / Your problem should look like:
Third, add x to both sides. / Your problem should look like:
Fourth, simplify 6x - 12 + x to get 7x - 12. / Your problem should look like:
Fifth, add 12 to both sides. / Your problem should look like:
Sixth, add -2 + 12 to get 10. / Your problem should look like:
Seventh, divide both sides by 7. / Your problem should look like:
Eighth, switch your sides. / Your problem should look like:
Answer: x =
Answer as decimal: 1.4286
Answer:
b. between .025 and .05
Step-by-step explanation:
Previous concepts and notation
The chi-square test is used to check if the standard deviation of a population is equal to a specified value. We can conduct the test "two-sided test or a one-sided test".
represent the sample mean
n = 30 sample size
s= 0.2 represent the sample deviation
the value that we want to test
represent the p value for the test
t represent the statistic
significance level
State the null and alternative hypothesis
On this case we want to check if the population standard deviation is less than 0.027, so the system of hypothesis are:
H0:
H1:
In order to check the hypothesis we need to calculate the statistic given by the following formula:
This statistic have a Chi Square distribution distribution with n-1 degrees of freedom.
What is the value of your test statistic?
Now we have everything to replace into the formula for the statistic and we got:
What is the approximate p-value of the test?
The degrees of freedom are given by:
For this case since we have a right tailed test the p value is given by:
And the best option would be:
b. between .025 and .05