Select the correct answer.
1 answer:
The inverse function of f(x) is and the domain is x > 6
The function is given as:
f(x) = x^2 + 6
Rewrite as:
y = x^2 + 6
Swap x and y
x = y^2 + 6
Subtract 6 from both sides
y^2 = x - 6
Take the square root
Rewrite as:
Hence, the inverse function of f(x) is and the domain is x > 6
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Answer:
see explanation
Step-by-step explanation:
Assuming the fractions are being multiplied
Factorise the denominators of both fractions
x² - 3x - 10 = (x - 5)(x + 2)
x² + x - 12 = (x + 4)(x - 3)
The product can now be expressed as
×
Cancel (x - 5) and (x + 2) on the numerators/ denominators, leaving
=
We are asked to determine the correlation factor "r" of the given table. To do that we will first label the column for "Quality" as "x" and the column for "Easiness" as "y". Like this:
Now, we create another column with the product of "x" and "y". Like this:
Now, we will add another column with the squares of the values of "x". Like this:
Now, we add another column with the squares of the values of "y":
Now, we sum the values on each of the columns:
Now, to get the correlation factor we use the following formula:
Where:
Now we substitute the values, we get:
Solving the operations:
Therefore, the correlation factor is 0.858. If the correlation factor approaches the values of +1, this means that there is a strong linear correlation between the variables "x" and "y" and this correlation tends to be with a positive slope.
