题目
题目

PRECALC141-033 1.3 Practice Problems

单项选择题

Givenf(x)= x 3 −4, find the inverse.

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标准答案
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思路分析
First, I restate what is given and what is being asked to ensure we’re examining the same problem. The problem appears to define a function f(x) that looks like f(x) = x^3 - 4, and asks for its inverse. Next, I note that the provided answer field in the data shows '3(x+4)' as a proposed answer, but there are no answer choices given in answer_options to evaluate against. To find the invers......Login to view full explanation

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类似问题

Find the domain and range of the inverse of the given function. f(x) =

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

Question text Find the inverse function of the exponential function [math: f(x)=2e5x−2+1]\displaystyle f(x)={2\,e^{5\,x-2}+1}. Note: Type [math: ln(a)] to enter [math: loge(a)]log_{e}(a). [math: f−1(x)=]f^{-1}(x)=[input] Check Question 7

Question text Find the inverse function of the exponential function [math: f(x)=6e2x−4+1]\displaystyle f(x)={6\,e^{2\,x-4}+1}. Note: Type [math: ln(a)] to enter [math: loge(a)]log_{e}(a). [math: f−1(x)=]f^{-1}(x)=[input] Check Question 7

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