5 Let f be the onetoone function Find the inverse function a

5. Let f be the one-to-one function. Find the inverse function: a) f(x) = 2x31 b)f(x) = V2x + 3 6. Sketch the graph of the piece-wise defined function and state the domain and range of f(ax) x +1 if -1sxs g(x)\"(3 if x>1 b) log+108216 as a sum and/or difference of logarithms. Simplify 7. Evaluate : a) log5250-logs 2, , as a sum and/or difference oflogarithms,Simplify c) Express logb( Solve for x and check the solution: a) logs& + 12) + log3(x + 4) = 2 , ) 8, b) Solve for x: 2x-1 = 3x 9, Perform the following transform ations of f(x) = log(x) a) Shift f(x) 3 units up, b) Shift the result of (a) 2 units left. c) Reflect the result of (b) about the x-axis. 10. Graph the following function with respect to the base functionfx) 2 g(x) =-(x-1)2 + 1 . State the domain and range of g(x).

Solution

5.a. f(x)=y= (x+3)/(2x-1)

switching x and y

x=(y+3)/(2y-1)

2xy -x =y+3

y(2x-1)= 3+x

y= (3+x)/(2x-1)

f^-1(x) = (3+x)/(2x-1)

b. f(x) = y =sqrt(2x+3)

switching x and y

x=sqrt(2y+3)

2y+3=x²

y=(x²-3)/2

f^-1(x) =(x²-3)/2