Question

For each of the following functions, f : R ? R state whether they are one-to-one, onto, both or neither. Use the following key: a neither 1-1 nor onto b 1-1 but not onto c onto but not 1-1 d both 1-1 and onto = bijective = invertible 1. f(x) = x(x - 7)(x + 7) 2. f(x) = |x| 3. f(x) = sin(x) 4. f(x) = x^3 + 7 5. f(x) = x + 8|x| 6. f(x) = e^x 7. f(x) = x^2 + 3

          For each of the following functions, f : R ? R state whether they are one-to-one, onto, both or neither. Use the following key:
a neither 1-1 nor onto
b 1-1 but not onto
c onto but not 1-1
d both 1-1 and onto = bijective = invertible
1. f(x) = x(x - 7)(x + 7)
2. f(x) = |x|
3. f(x) = sin(x)
4. f(x) = x^3 + 7
5. f(x) = x + 8|x|
6. f(x) = e^x
7. f(x) = x^2 + 3

For each of the following functions, f : R ? R state whether they are one-to-one, onto, both or neither. Use the following key:
a neither 1-1 nor onto
b 1-1 but not onto
c onto but not 1-1
d both 1-1 and onto = bijective = invertible
1. f(x) = x(x - 7)(x + 7)
2. f(x) = |x|
3. f(x) = sin(x)
4. f(x) = x^3 + 7
5. f(x) = x + 8|x|
6. f(x) = e^x
7. f(x) = x^2 + 3

Added by Andrea M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Rukhmani Jain

01/24/2022

Step 1

**Step 2:** For the function \(f(c) = |r|\): This function is neither one-to-one nor onto. **Step 3:** For the function \(f(z) = \sin(z)\): This function is neither one-to-one nor onto. **Step 4:** For the function \(f(r) = 2 + 7\): This function is onto but Show more…

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For each of the following functions, f : R → R, state whether they are one-to-one, onto, both, or neither. Use the following key: neither 1-1 nor onto, 1-1 but not onto, onto but not 1-1, both 1-1 and onto = bijective = invertible. 1. f(x) = x(x - 7)(x + 7) 2. f(x) = |x| 3. f(x) = sin(x) 4. f(x) = x^3 + 7 5. f(x) = x + 8|x| 6. f(x) = e^x 7. f(x) = x^2 + 3