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

[sonya]

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

 

[HallsofIvy]

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?

 

[sonya]

well...f(x)=10 when x=0
but i don't c ne relation btwn that and the inverse...

 

[HallsofIvy]

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

 

[sonya]

thats it?...how come it looks so simple now?...neways thanks 4 clearing things up!...