If a function is one-to-one, then its inverse exists. For any function, each member of the domain corresponds to one, and only one, member of the range. If f:x → y is a function, then y → x is also a function. We call this function the inverse function of f, written f-1:y → x f y f-1 FIGURE Q2 Based on polynomial equations, k(x) = mx? + nx + c , where {m, n,c eR} answer the following questions. Express a standard form of k(x) in terms of m,n and c Use graphical approach and the relevant test to determine whether a function is one-to-one or not. • Express an inverse function of k(x) in terms of m, n and c Determine TWO conditions that make inverse of k(x) exists Sketch the graphs of the k(x) and k-1(x) for both conditions. Specify the domains and ranges of the k(x) and k-(x) for both conditions. 2.
If a function is one-to-one, then its inverse exists. For any function, each member of the domain corresponds to one, and only one, member of the range. If f:x → y is a function, then y → x is also a function. We call this function the inverse function of f, written f-1:y → x f y f-1 FIGURE Q2 Based on polynomial equations, k(x) = mx? + nx + c , where {m, n,c eR} answer the following questions. Express a standard form of k(x) in terms of m,n and c Use graphical approach and the relevant test to determine whether a function is one-to-one or not. • Express an inverse function of k(x) in terms of m, n and c Determine TWO conditions that make inverse of k(x) exists Sketch the graphs of the k(x) and k-1(x) for both conditions. Specify the domains and ranges of the k(x) and k-(x) for both conditions. 2.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:2.
If a function is one-to-one, then its inverse exists. For any function, each member
of the domain corresponds to one, and only one, member of the range. If f:x y
is a function, then y → x is also a function. We call this function the inverse function
of f, written f-1:y→ x
f-1
FIGURE Q2
Based on polynomial equations, k(x) = mx² + nx + c, where {m, n, c eR} answer
the following questions.
• Express a standard form of k(x) in terms of m,n and c
Use graphical approach and the relevant test to determine whether a function
is one-to-one or not.
Express an inverse function of k(x) in terms of m,n and c
Determine TVWO conditions that make inverse of k(x) exists
Sketch the graphs of the k(x) and k-1(x) for both conditions.
Specify the domains and ranges of the k(x) and k-1(x) for both conditions.
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