Αποτελέσματα Αναζήτησης
An inverse function is a second function which undoes the work of the first one. In this unit we describe two methods for finding inverse functions, and we also explain that the domain of a function may need to be restricted before an inverse function can exist.
From the graph of y = x2 ± 8 below, you can see that the inverse relation has domain ( ± , ) and range [8, ). By restricting the domain of the inverse relation to [0, ), the domain and range of f are equal to the range and
Inverse Functions and Relations. 2. {(0, –9), (5, –3), (6, 6), (8, –3)} Find the inverse of each function. Then graph the function and its inverse. 3. y = 4. 6. g(x) = 2x – 1 . 4. f(x) = 3x. 1. 7. h(x) = x . 5. f(x) = x + 2. 2. 8. 4. y = x + 2. 3. Determine whether each pair of functions are inverse functions. Write yes or no. 9. f(x) = x + 6 .
Inverse Relations and Functions. Graph each relation and its inverse. 1. x 1 3. y 5. 3. 1 2. y 5 x 1 5. 2. 3. y = 2x 5 +. 4. y = 4x2 5. y 5 1 x2. 2. Find the inverse of each function. Is the inverse a function? 6. y 5 2 x2. 3. 7. y = x2 + 2. 8. y = x + 2. 9. y = 3(x + 1) 10. y = -x2 - 3. 11. y = 2x - 1. 12. y = 1 - 3x2. 13. y = 5x2.
Inverse Relations and Functions. 11.1 OBJECTIVES. Find the inverse of a relation. Graph a relation and its inverse. Find the inverse of a function. Graph a function and its inverse. Identify a one-to-one function. Let’s consider an extension of the concepts of relations and functions discussed in Chapter 3. Suppose we are given the relation.
Determining the inverse of a function: 1. Verify that f(x) is a one-to-one function. (If not, its inverse is not a function.) 2. Replace with y and exchange all x’s and y’s. 3. Solve for y. 4. Replace the new y with . (Only if is actually a function.) Example 1: If f x x( ) 3 2 , determine the inverse of the function. Example 2: If () 31 x ...
Inverse Relations. Two relations are inverse relations if and only if one relation contains the element (b, a) whenever the other relation contains the element (a, b). If f(x) denotes a function, then f 1(x) denotes the inverse of f(x). However, f 1(x) may not necessarily be a function.
