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Homework Assignment 1 Inverses
Find the inverse of each relation and determine whether the inverse is a function. Answer (A) if the
inverse IS a function or answer (B) if the inverse is NOT a function.
1. {(2, 4), ( 3, 1), (2, 8)} 2. {( 1, 2), ( 3, 2), (1, 4), (0, 6)}
3. {( 1, 3), (1, 1), (1, 3), (1, 1)} 4. {(6, 11), ( 2, 7), (0, 3), ( 5, 3)}
Determine whether the given function is one-to-one. Answer (A) if the function IS a one-to-one oranswer (B) if the function is NOT one-to-one.
5. y = 6 6. y = 4x 7. f(x) = 4x + 4
8. g(x) = x + 2 9. f(x) = x
3/5
10. g(x) = x
4/5
2
11. y = x2 9 12. y = (x 9)2 13. f(x) =
14. y = x2
+ 1 15. y = (x 4)3
16. y = (x + 2)5
3
Determine whether the given functions are strictly monotonic. Answer (A) if the function IS a strictly
monotonic or answer (B) if the function is NOT strictly monotonic.
17. f(x) = x3 3 18. f(x) = 4x 8
19. f(x) = 5x + 20 20. f(x) = (x + 1)2
21. f(x) = 22. f(x) = x2 3
Answer the following:
23.The function is invertible. Give .a. -1b. 0c.
1d. 1/2
e. None of these.24.The function is invertible. Give .
a. 1/2b. -2c. 2d. -1/2e. None of these.
2x 1
3
x
( ) 2 3 f x x= + 1(3)f
( ) 2 3 f x x= +( )1
df x
dx
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25.The function is invertible. Give the slope of the tangent line to the graph ofat x = 2.
a. -1/2b. 4c. 1/4d. 2e. None of these.
26.The function is invertible. Give .a. 1b. 2c. -1d. 1/2e. None of these.
27.The function is invertible. Give the slope of the tangent line to the graphof at x = 2.
a. 1b. 2c. -1d.
1/2e. None of these.
28.The graph of f is shown below. Determine whether f is invertible.
a. The function is invertible.b. The function is not invertible.
3( ) f x x x= +
1( )f x
3( ) f x x x= + 1(2)f
( ) 2 3 f x x= +
1( )f x
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29.The graph of f is shown below. Determine whether f is invertible.
a. The function is invertible.b. The function is not invertible.
30.Determine whether is invertible.c. The function is invertible.d. The function is not invertible.
31.The function is invertible. Give .a. -1b. -2c. 1/2d. 2e. 1f. None of these.
32.The function is invertible. Give the y-intercept for the tangent lineto the graph of at x = 0.
a. -3b. -2c. -1d. 1e. 2f. None of these.
4 3( ) 3 1 f x x x= + +
5 3( ) 3 1 f x x x x= + + + ( )1
'(1)f
5 3( ) 3 1 f x x x x= + +
1( )f x
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33.Suppose and . Give the slope of the tangent line to the graph ofat x = 3.
a. -3b. -2c. 1d. 2e. 3f. None of these.
( )
1
' (1) 1/ 3f
=
( )3 1f=
( )f x