Q |Page view A Read aloud T Add text A Evaluate the following (without a calculator). (a) log 1000 (b) log 10-342 (c) In(e") Solve for x (use log where necessary) 4 -8 (b) 2- + * = 3Use the properties of logarithms to express the following as sum, difference or constant multiple. In4. Solve for x and check for any extraneous roots. (a) log , (x - 1) = 2 (b) log 10 (x +3) + log 10 (x) = 15. A 20-foot ladder leaning against a wall makes an angle of 30 with the ground, how high up the wall does the ladder reach the wall? , draw a diagram/Show that the functions fox) - x' + 3 and g(x - x-3 are inverses by verifying that fig(x)) = x and g(f (x)) =x f (8 (x) - /(V/x-1) Find the inverse function of f(x) - - -x - 5 and describe its domain and range.Suppose f and g are inverse. If f(3) - 5, find g(5) Le fbe defined as f(xx) = _. Find f ' (3) in two different ways. One Way: Find f" and then computef (3) Another way : Solve for x f) =x NL -3 2x +15 . Let f ( x ) = 2 Vx + 3 (a) Show that f is one-to-one. 5 ( 2 ) = \\ + 3 2 (b) Find the inverse function of f(xx).(c) Describe the domain and range of the inverse function (d) State the relation between the graphs of the function and its inverse? Sketch the graphs of f and f' on the same pair of axes 10 9 NW 2 3Solve the following equation for x. The domain of both f and its inverse is the set of all real numbers and f (5) = 3. 7+3f (2x-1) =12 (2x -1) =5 f(f (2x -D) =/(5) Given /(5) =3Given f (x) = 2x + 3 (a) find (b) describe domain and range off c) Show that f (f(x)) -x and / 6 (x))=x a f(x) 2x + 3 x -1 Domain off. x = 1 Range: y * 2 2x + 3 x - I(b) Domain: x + 2 Range: y = 1 (c) 2x +3 times the numerator and denominator by( x - 1) 2x + 3 + 3x - 3 2x+3 - 2x + - x =X1. For each function, (a) Sketch the graph (b) Describe the domain and range (c) State and show the x-intercept and y-intercept (ifany) (d) State and show any asymptote (e) Determine over what interval the graph is increasing or decreasing. (ii) fx) = 2* (i) f(x) = 2* Domain: Domain: Range: Range: x-intercept: x-intercept: y-intercept: -intercept: Horizontal Asymptote: Horizontal Asymptote: Increasing: Increasing: Decreasing: Decreasing: acer(iv) g(x) =ex (iii) g(x) = er Domain: Domain: Range: Range: x-intercept: x-intercept: y-intercept: V-intercept: Horizontal Asymptote Horizontal Asymptote: Increasing: Increasing: Decreasing: Decreasing: acer\f3. Let f(x) = 2, show that S(x + h) - f(x) Find the value of a and b in the function (x) - be , it/(-1) =15 and /(2) - 5/9.Show that /(x) = 2-e " is an even function. Sketch f and describe its symmetry 5. 6. Let /(r) 2 +2 and g(x) 2 2 Compute / - 2.