Solving an Inverse Problem with f(x)=5+2x+5e^x

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Homework Help Overview

The discussion revolves around the problem of finding the inverse of the function f(x) = 5 + 2x + 5e^x, specifically determining f^-1(10). Participants express challenges with inverse problems and seek guidance on how to approach this particular question.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the difficulty of finding an inverse function when the variable appears in both an exponent and as a base. There is an exploration of the relationship between the function value and its inverse, particularly focusing on the specific case of f(x) = 10.

Discussion Status

The conversation has progressed towards clarifying the definition of inverse functions. One participant has identified a specific value of x that satisfies f(x) = 10, leading to a clearer understanding of the relationship between f and its inverse. However, there remains a lack of explicit consensus on the broader implications of this understanding.

Contextual Notes

Participants are navigating the complexities of inverse functions and the specific constraints of the problem, including the challenge posed by the function's structure. There is an acknowledgment of the confusion that arises from the definitions and properties of inverse functions.

sonya
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i keep getting stuck on these inverse problems...

the question is

let f(x)=5+2x+5e^x
f^-1(10)=?

i keep messing up on these problems and now I am not really sure where exactly 2 start...i know i got to find the inverse but i would appreciate some help on getting started on this problem...thx
 
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There is no way to algebraically find the inverse function to f(x)- not with x both in the exponent and as a base.

However, the problem does NOT ask you to find "f-1", it only asks you to find "f-1(10)".

Can you think of a value of x such that f(x)= 10 and what does that have to do with the problem?
 
well...f(x)=10 when x=0
but i don't c ne relation btwn that and the inverse...
 
Then I think we've discovered WHY you keep "getting stuck on these inverse problems"! That's the DEFINITION of inverse!

Two functions (call them f and g) are "inverse" to each other (here's the "formal" definition) if and only if f(g(x))= x and g(f(x))= x for all x.

If f(x)= y, then f-1(f(x))= f-1(y)= x.

Since f(0)= 10, f-1(10)= 0.

Whenever f(a)= b, then f-1(b)= a.

if f: x-> y then f-1y-> x
 
thats it?...how come it looks so simple now?...neways thanks 4 clearing things up!...
 

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