Select the correct answer. What is the domain of the function f(x) = 4x − 16? all real numbers all positive real numbers all pos
2 answers:
<h3>Answer:</h3>
The domain of the function f(x) is:
All real numbers.
<h3>Step-by-step explanation:</h3>We are given a linear function f(x) in terms of the variable 'x' as:
Now we are asked to find the domain of the function f(x).
<em>We know that the domain of a function is the possible set of the x-values where the function is well defined that is the function does not gives a absurd result.</em>
As we know that the polynomial function i.e. here a linear polynomial function is defined all over the real axis and is also continuous there.
The graph of this linear function will be a straight line.
Hence, the domain of the given function f(x) is:
All real numbers.
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Answer:
Step-by-step explanation:
We have to see how the canonical vectors are transformed throught T. Lets first define T in any basis.
Since T is a reflection, then any element of the line y = x/2 if fixed by T. Therefore T(2,1) = (2,1).
On the other hand, any vector perpendicular to the line direction should be sent to its opposite value. We can take, for example, (-1,2) (note that the scalar product (2,1) * (-1,2) = -2+2 = 0). As a consecuence T(-1,2) = (1,-2). We have
- T(2,1) = (2,1)
- T(-1,2) = (1,-2)
By summing the first vector with the double of the second one we get, using linearity
T(0,5) = T( (2,1) + 2(-1,2)) = T(2,1) + 2T(-1,2) = (2,1) + 2(1,-2) = (4,-3)
Hence, T(0,1) = (4/5,-3/5)
Now, we take the second vector and substract it the double of the first one (to kill the second variable)
T(-3,0) = T( (-1,2) - 2*(2,1) ) = T(-1,2) -2T(2,1) = (1,-2)-2(2,1) = (-3,-4)
Therefore, T(1,0) = (1,4/3)
The matrix A induced by T has in its first column T(1,0) and in its second column T(0,1). We conclude that