Question

please.show work and answer full.question. this js discrete math.

1. Determine whether each of the functions is one-to-one and/or onto. a. f:R - R, f(x) = 19(x) = log2(x) one-to-one onto onto one-to-one b. f:N NX N, f(x) = (x,x) onto one-to-one c. f:R+ (-1,1), f(x) = cos(x) one-to-one onto d. 8:[2,3) –> (0, +), f(x) = ***

Answer 1

Salution Determine each of the function is one-one and for onto fit R, f(W = logen If n E (-os, o then function is not defined So fiRiR, fox) = laag & is not Function Hence it is not neither one to one nor onto. fi N NXN, f(x) = (1, 2) Now From one-one If flug = f(y) = ge=y. where noy EN So f(x) = fly) - (2, 4) = (y J) So it is one-one Nowe For onto ty E ENXN 3 n sit flw= y. het y = (1, 2) then u Hence it is not onto. sit f(n)= y.

º fill [1,1] , fin) = 10 Now For one-one. If f(x) = fly) - re-y where njer Nowe Take fru) - fly) - GX = Gey. xty (if(0) = 1 2 f(2x) = 1) So it is not one-one. Now For onto. & y E [1,1] u sit f(x) = y Gr=y de ! So it is onto ② f. 23) – Co,es), fox) = x - For one-one. If from a fly) = x=y where my (2, 3) Nove Take flu = fly) 22 So it is one-one. Now for ontro & J E [o,as) In sit f(n)=y. - 2 = y = -2 = 34-ny Nony = 34-2 = n = at Ling & Con ity So it is onto Ausmer -
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