Pre-Calc Homework Solutions 25

Pre-Calc Homework Solutions 25 - 5 2 x 1 3 y 2 3 5 2 x } y...

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7. [ 2 10, 10] by [ 2 10, 10] Yes, the function is one-to-one since each horizontal line intersects the graph at most once, so it has an inverse function. 8. [ 2 10, 10] by [ 2 10, 10] No, the function is not one-to-one since (for example) the horizontal line y 5 0 intersects the graph twice, so it does not have an inverse function. 9. [ 2 10, 10] by [ 2 10, 10] No, the function is not one-to-one since (for example) the horizontal line y 5 5 intersects the graph more than once, so it does not have an inverse function. 10. [ 2 5, 5] by [ 2 20, 20] Yes, the function is one-to-one since each horizontal line intersects the graph only once, so it has an inverse function. 11. [ 2 10, 10] by [ 2 10, 10] No, the function is not one-to-one since each horizontal line intersects the graph twice, so it does not have an inverse function. 12. [ 2 9, 9] by [ 2 2, 10] Yes, the function is one-to-one since each horizontal line intersects the graph at most once, so it has an inverse function. 13. y
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Unformatted text preview: 5 2 x 1 3 y 2 3 5 2 x } y 2 2 3 } 5 x Interchange x and y . } x 2 2 3 } 5 y f 2 1 ( x ) 5 } x 2 2 3 } . Verify. ( f + f 2 1 )( x ) 5 f 1 } x 2 2 3 } 2 5 2 1 } x 2 2 3 } 2 1 3 5 ( x 2 3) 1 3 5 x ( f 2 1 + f )( x ) 5 f 2 1 (2 x 1 3) 5 } (2 x 1 2 3) 2 3 } 5 } 2 2 x } 5 x 14. y 5 5 2 4 x 4 x 5 5 2 y x 5 } 5 2 4 y } Interchange x and y . y 5 } 5 2 4 x } f 2 1 ( x ) 5 } 5 2 4 x } Verify. ( f + f 2 1 )( x ) 5 f 1 } 5 2 4 x } 2 5 5 2 4 1 } 5 2 4 x } 2 5 5 2 (5 2 x ) 5 x ( f 2 1 + f )( x ) 5 f 2 1 (5 2 4 x ) 5 } 5 2 (5 4 2 4 x ) } 5 } 4 4 x } 5 x 15. y 5 x 3 2 1 y 1 1 5 x 3 ( y 1 1) 1/3 5 x Interchange x and y . ( x 1 1) 1/3 5 y f 2 1 ( x ) 5 ( x 1 1) 1/3 or 3 x w 1 w 1 w Verify. ( f + f 2 1 )( x ) 5 f ( 3 x w 1 w 1 w ) 5 ( 3 x w 1 w 1 w ) 3 2 1 5 ( x 1 1) 2 1 5 x ( f 2 1 + f )( x ) 5 f 2 1 ( x 3 2 1) 5 3 ( x w 3 w 2 w 1 w ) w 1 w 1 w 5 3 x 3 w 5 x Section 1.5 25...
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