OGRAPHS AND FUNCTIONS Variable expressions as inputs of functions: Problem type 2 9 The function h...
OGRAPHS AND FUNCTIONS Finding a difference quotient for a linear or quadratic function f(x+h)-f(x) Find the difference quotient h where h#0, for the function below. F f(x) = -372 -4x+9 Simplify your answer as much as possible. $(x + n) - f(x) h I
DOMAIN SHOULD HAVE 3 parts E OGRAPHS AND FUNCTIONS Composition of two rational functions 13 2 and g(x) find the composition fog and simplify your answer as much as possible. Write the domain using interval x+3 For the functions f) notation rain lol (0) (0) DVD (0) 00) CO -00 Domain off: ? 6 X
OGRAPHS AND FUNCTIONS Sum, difference, and product of two functions Suppose that the functions g and h are defined for all real numbers x as follows. g(x) = 4x+3 h(x)=x+6 Write the expressions for (h-g)(x) and (h+g)(x) and evaluate (h.g)(3). X (1 + 3)(x) = 1 (h.:)) = 0
= OGRAPHS AND FUNCTIONS Inverse functions: Linear, discrete The one-to-one functions g and h are defined as follows. g(x) = 4x -9 h={(3, 5), (4, - 7), (5, 4), (8, 1), (9, 3)} Find the following. DO 8-'(x) = 0 (es)6) = 0 X Ś ?
O GRAPHS AND FUNCTIONS Composition of a function with itself Suppose that the functions fand g are defined as follows. f(x)--, x#0 g(x)-x2-9 Find the compositions f fand g'g. Simplify. your answers as much as possible. Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the doma Explanation Check
Evaluate the following function at the values t+2 and t+h. 3 g(t) 5t-8t g(t+ 2) (Simplify your answer. Type an expression using t as the variable. For the following function, determine the difference quotient x+h)- f(x) h f(x) 5x-9x fix+h)- fx) h (Simplify your answer. Use integers or fractions for any numbers in the expression.) .Z.O Find the x-intercept(s) and the y-intercept of the function P(x)-3x +22x2 +7x Select the correct choice below and fill in any answer boxes within...
For the given functions f and g, complete parts (a)-(h). For parts (a)-(d), also find the domain. 3x +7 f(x) = 7x-3 9(x) = 6x 7x-3 (a) Find (f+g)(x). (*+g)(x)=(Simplify your answer.) What is the domain off+g? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The domain is {x}. (Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) O B....
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...
please The functions f, g, and h are defined as follows. X+6 =52o 8(x)=-6+ Vx-2 h(x)= |x-1|| Find f(a), 3(5), and 1 () Simplify your answers as much as possible. x 5 ? I Don't Know
2. (16 points) In this problem, you will be a math detective! Some of the symbols and functions may not be familiar to you, but with a little digging, reading, and observ- ing, you'll be able to figure them out. Your task is to simplify each of the following expressions as much as possible, without using a calculator (either hardware or software. Do not approximate. Express all rational numbers as improper fractions. You may assume that n is an nteger...