题目
题目

MCD2130 - T2 - 2025 MCD2130 Sample Test 3

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Question text Find the inverse function of the exponential function [math: f(x)=7e2x−4−2]\displaystyle f(x)={7\,e^{2\,x-4}-2}. Note: Type [math: ln(a)] to enter [math: loge(a)]log_{e}(a). [math: f−1(x)=]f^{-1}(x)=[input] [math: (in(x+27))+42] \frac{\left({\it in}\left(\frac{x+2}{7}\right)\right)+4}{2}

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思路分析
We are given the function f(x) = 7 e^{2x - 4} - 2 and asked to find its inverse. First, set y = f(x) to relate x and y: y = 7 e^{2x - 4} - 2. Step 1: Solve for the exponential term. Add 2 to both sides: y + 2 = 7 e^{2x - 4}. Step 2: Isolate the......Login to view full explanation

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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

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