题目
MATH*2415*W16 Practice Quiz- Requires Respondus LockDown Browser
单项选择题
Find the domain and range of the inverse of the given function. f(x) =
选项
A.Domain: [4, ∞); range: [0, ∞)
B.Domain and range: all real numbers
C.Domain: [4, ∞); range: [4, ∞)
D.Domain: [0, ∞); range: [4, ∞)
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标准答案
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思路分析
To determine the domain and range of the inverse, first recall the original function f(x) = sqrt(x - 4).
Since the square root requires its input to be nonnegative, the domain of f is x ≥ 4. The output of f is a nonnegative number, so the range of f is y ≥ 0.
When forming the inver......Login to view full explanation登录即可查看完整答案
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类似问题
Problem: Find the inverse for the function 𝑓 ( 𝑥 ) = 3 𝑥 + 1 2 𝑥 − 4 . Suppose a student writes the following solution. Is it correct? Line 1: Write 𝑦 = 3 𝑥 + 1 2 𝑥 − 4 and solve for 𝑥 . Line 2: 𝑦 ( 2 𝑥 − 4 ) = 3 𝑥 + 1 Line 3: 2 𝑥 𝑦 − 4 𝑦 = 3 𝑥 + 1 Line 4: 2 𝑥 𝑦 − 3 𝑥 = 1 + 4 𝑦 Line 5: 𝑥 ( 2 𝑦 − 3 ) = 1 + 4 𝑦 Line 6: 𝑥 = 1 + 4 𝑦 2 𝑦 − 3 Line 7: Now interchange variables: 𝑦 = 1 + 4 𝑥 2 𝑥 − 3 Line 8: Therefore 𝑓 − 1 ( 𝑥 ) = 1 + 4 𝑥 2 𝑥 − 3 Line 9: Simplify: 𝑓 − 1 ( 𝑥 ) = 𝑥 + 4 2 − 3 𝑥 a) Is the above solution correct? If not, in which line is the first error? (If there is more than one error, select the line where the FIRST error occurs.) [ Select ] First error is in Line 2. First error is in Line 9. The solution is correct. First error is in Line 1. First error is in Line 7. First error is in Line 4. First error is in Line 6. First error is in Line 3. First error is in Line 5. First error is in Line 8. b) What is the correct final answer to the problem? [ Select ] y = (x+1) / (2-3x) y = (1+4x) / (1-6x) y = (x+4) / (2-3x) None of the other options y = (1+4x) / (2x-3) c) What is the domain of 𝑓 − 1 ( 𝑥 ) ? [ Select ] All real numbers except 3/2 All real numbers except -4 All real numbers except -1/4 All real numbers except 1/6 All real numbers except 2/3
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