Question 1 The functions f(x) g(x) and h(x) are defined as follows: f(x) = e* XER...
1. Given f(x) = et XER g(x) = 3lnx x > 0,x & IR a) Find an expression for fg(x), simplifying your answer [2] b) Show that there is only one real value of x for which fg(x) = gf(x) (6) 8 Marks
Question 2 The function r) is defined by 3(x + 1) 1 f12r + 71-4 1+4 () (111) 13 marks Show that f(x)= [4 marks) Find (3) Find the domain off- [2 marks] Given that g(x) = In(x + 1) Find the solution of r if fg(x) = 5, by leaving your answer in terms of e exponential function) [4 marks) (b) Sketch the graph of the function, In)-1-cosx). not by plotting points, but starting with the graph of a...
25 (4 comple The functions f and g are defined as f(x) = 8x - 5 and g(x) = - 6x?. a) Find the domain of f, g, f+g, f-g, fg, ff, and g' b) Find (f+g)(x), (f-g)(x), (fg)(x), (ff)(x), 0 (x), and (0)612 a) The domain offis I. (Type your answer in interval notation.) The domain of g is (Type your answer in interval notation.) The domain off+ 9 (Type your answer in interval notation.) The domain off-gis (Type...
Suppose that the functions f and g are defined as follows. 5x +2 Find f+g and fg. Then, give their domains using interval notation. Domain of f+g Domain of fg
Suppose that the functions f and g are defined as follows. f(x)=-4x+5 g(x) = 2x+1 Find f-g and . Then, give their domains using interval notation. 0 0 (-8)(x) = 0 0 .6 (0,0) [0,0] Domain off-g: 0 OVO (0,0] [0,0) Ø 00 -00 ()(w) = 0 5 ? Domain of I bo
f(x) = 2x -1 g(x) = Square root (x-1) Find the domain of f, g, f+g, f-g, fg, ff, f/g, and g/f. I actually got the answers to the domain of f and g, but i'm confused on how to find the others based on just f and g. Like for the domain of f, I got (-infinity, positive infinity) then for the domain of g, (negative infinity, 1) U (1, positive infinity)
2 2. For function h(x) - a. Find (-1) b. Find the domain of h(x), write your answer in set-builder notation. 2 c. For function (x) h'(x) and state the domain and range of h'(x). 3. a. What is the relationship between the graph of a function and the graph of its inverse? b. Graph the function (x) = V1 – 3 and its inverse on the same coordinate system. Determine at least 3 points on each graph. Label each...
please answer to the question in the figure. Find each of the following functions. rx) = V5-x, g(x) = VX2-4 (a) fg State the domain of the function. (Enter your answer using interval notation.) (b) f-9 State the domain of the function. (Enter your answer using interval notation.) (c) fg State the domain of the function. (Enter your answer using interval notation.) (d) fig State the domain of the function. (Enter your answer using interval notation.) x+2 (a) fog (fo...
Suppose that the function F & G are defined as follows Suppose that the functions f and g are defined as follows. f(x) = 5-2x? g(x) = 2 - 6x (a) Find ( 2 )(-1). (a) Find (b) Find all values that are NOT in the domain of If there is more than one value, separate them with commas. (b) Value(s) that are NOT in the domain of
The function f is defined as follows. f(x)- 4x-3 if x21 (a) Find the domain of the function. (b) Locate any intercepts. (c) Graph the function. (d) Based on the graph, find the range. (e) Is f continuous on its domain? The function f is defined as follows. f(x)- 4x-3 if x21 (a) Find the domain of the function. (b) Locate any intercepts. (c) Graph the function. (d) Based on the graph, find the range. (e) Is f continuous on...