Question

400 Exp l io and Lageri F CHAPTER s EXAMPLE Gren that a)-Sx+8,we compotnd so show that 401 vere Fanii Solution We ed ( n)and (ff )nd check to w h . f) opt the epion by subutituring and plotring poit 44 The et e meph a he liny se e pph ef ts vera isx n-r) 12. y 1 (Sx+8)- 14. x y 4 16 2l rS+) (f )-() Gem the fnction f. prve dhat f is one-to-ene ing d ti of a one-to-ane fannion onp 394 +8 18. f)4-2 a)--6 20. fx)V a) Restricting a Domain In the cae in which the invers of a fnction is not a fnctin he ln of the function can be restricted to allow the imverse to be a fandes consider the function fx) -2.h is ot ene-to-n The ge Gee the fanctiee g.prove that g is not ane-te-oe wethe definition of a one-to-ene function on p a fa)-1- showa at left. 22 )-3+1 Suppose that we had tried to find a formula for the ivere aes 2 glx) Graph the fnonand derne whether the function is one-- ing the herialine st 33. S y -2 y-2 +2-y t Vx+ 2-y Replacing fx) wih y Inerchangling x and y 24 (x) 34 flx)3 4 6 x)--2 3 fx) 35. )-1- Ching the horizontal-lise teat, determine whether the fnction is one-te-ane 25. fla)-2.7 Selving for y 3. fle)-x+2 This is not the equation of a function. An input of, say, 2 would yidld he outputs,-2 and 2. In such cases, it is convenient to consider art d fanction by restricting the domain of f(x). For example, if we m the domain of f(x)-x-2 to nonnegative numbers, then its ie is a function, as shown with the graphs of f(x)--2,x2 )-Vx +2 at left. (26) f(x)-2" 2 x+3 40. fa) 42. x)- 3 fx-a-2 for inputs x2 4 )Vs- Graph the fnction and in invere uing a aphing callt Ue an imes dwing frature, ifeailable. Find the demain and the nange of f and of f 46 fx)-27-1.08 flx)-- 45. fx) + 17 5.1 ef)-j-4 Exercise Set 22. fa)-4- 28x)--+11 2 56. fx) Find the inverse of the relation L ((7.8).(-2.8).(-4).(8-)) 2. (()(5.6).(-2-4) (-1-1)(-34)) (-13) (2.5).(-1,5). (2.0)) A a fd-V- St. f)--4xt 52. )-3-2z fa)--9 Find an equation of the inverse relation 5. yx- 6. 2+5y-4 7. xy- 8. y3x-5x+9 14

the ones with circle please

Answer 1

6 diverse of a Relation - Inverse of ordered pairs Relation = {(-1, 3), (2,5), (-3,5), (2,0)} Inverse = $13,-1), (5,2)., (5,-3), (0, 2)} 2 f(x) = 24 of f(a) = $4b). 2. so the function is -1. There is no Horizontal line which cuts the graph more than once so it is H Scanned with CamScanner

lo This function is not !-! since there is a horizontal line that hits the graph more than once : The tire hits the graph at A,B, e point Scanned with CamScanner