Is the set of functions f1(x) = ex + 2, f2(x) = ex − 4 linearly dependent or linearly independent on (−[infinity], [infinity])? Discuss. Since ex − 4 = ex + 2, we see that ex − 4 a constant multiple of ex + 2 and the set of functions is linearly .

not linearly independent

Step-by-step explanation:

Given:

- A set of function is given as follows:

                           f1(x) = e^(x + 2)

                           f2(x) = e^(x-4)

Find:

Is the set of functions f1(x) & f2(x) linearly dependent or linearly independent on (−[infinity], [infinity])?

Solution:

- Re-write the two functions in the form as shown below:

                           f1(x) = e^(x) * e^2

                           f2(x) = e^(x) * e^-4

- Divide the two functions f1(x) / f2(x):

                            f1(x) / f2(x) = [e^(x) * e^2] / [e^(x) * e^-4]

                            f1(x) / f2(x) = e^(6)

- The function f1(x) is e^6*f2(x) a scalar multiple we can say that two functions are not linearly independent.