Determine whether the following are linear transformationsfrom C [0, 1] into R1: L (f ) = [ f (0) + f (1)]/2

hove directly that the functions f1 (x) =1. fa(x) = x, and f2(x) = x2 are linearly independent on the whole real line. n me n functions f1, f2,..., fn are said to be linearly independent on the interval I provided that the identity Cif1 + C2f2 + .. + Cnfn =0 holds on I only when (1) - W art for constants C1, C2, .., Cn• Given, f1 (x) = 1, f2(x) = x, and fa(x) = x², the identity c, f, + c,f, + ... as, + Cnfn =0 can bewritten (0 CL= (-0. The current equation involves thee unknowns, c1. cɔ. and ca. Two more equations are needed in order to determine the Values of all three unknowns. How can these two equations be determined? Select the correct choice below and fill in the answer boxes to complete your choice. %3(1.0.JW nsilanoW Insbneqabni yhoenil ons r W aA O A. Determine the first and second derivatives of the current equation, with respect to x. The first derivative is (x)s (d.p.w nablandw eT B nebnoqab hsonil en enll isat s 0.0 gebou 3(d.p .W nelaniow erfT O The second derviative is =…

4. Show that the function f: R → R defined by f(x) = x² - 3x + 1 is not one-to-one.

Evaluate the function g(x, y) at the point (4, –8). x2 + y2 g(4, –8) =