Please help me with these following problems:(adsbygoogle = window.adsbygoogle || []).push({});

1.)Indicate whether each of the following functions is invertible in the given interval. Explain

a.) sech x on [0,infinity)

b.) cos (ln x) on (O, e^pie]

c.) e^(x^2) on (-1,2]

My work process for a: let y= sech x

how do i find x in terms of y for this eq. how do i isolate the x variable from sech x.

once I find that i can see if the positive values of x for the inverse function exist from 0 to infinity.

however, i need help finding the inverse function

My work process for b.) let y= cos (ln x)

I took the expotential of both sides to get

e^y= e^(cos*(lnx))

how do i isoloate e*(lnx) to equal x , since the lnx is a part of the cosine angle expression.. i need help here...

once i find the inverse equation, i can see if y values exists for the x values from 0 to e^pie... i need help finding the inverse equation first

My work process for c.) let = y= e^(x^2)

therefore taking the natural logarithm of both sides i get

ln y= ln (e^(x^2)

ln y= x^2

therefore x= sqrt (ln y)

therefore f^-1 (x)---> inverse function is f(x)= sqrt (ln x)

when subbing (-1,2] for x to determine if y values exist,

i find the inverse function doesn't exist under those limits since ln 0 is undefined

is this the correct approach to this problem.

Please help me with these problems!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Inverse Equation and if Values exist!

**Physics Forums | Science Articles, Homework Help, Discussion**