Trig question (1st explained ans=10pts!)?

Question

f(x) = 2 ^ x

then,

f ^ -1 (8) = __?__

How do you do f ^ -1 (x) questions?

Thank you so much!

Answer 1

The inverse of 2^x is y=log_2(x) because when you switc x and y you get:

x=2^y

take log_2 of both sides to solve for y.

Then plug in 8:

log_2(8)=y

8=2^y

2^3=2^y

y=3

Answer 2

let's rewrite this as :  f(x)=   y = 2^x

now  f^-1(x)  is equal to  1/f(x)   so  it's equal to  1/ (2^x)

and evaluated at x=8

so it's 1/(2^8)   or   1/256

good luck

Answer 3

This is a two step problem where they first want you to compute the inverse and then use the inverse at 8 for the final solution.

First compute the inverse:

y = 2^x

Change x and y and solve for y

x = 2^y

ln x = ln 2^y

ln x = y ln 2

y = ln x / ln 2

So,

f(-1) = ln x / ln 2

Now solve for the value of 8:

f(-1)(8) = ln 8 / ln 2

f(-1)(8) = 3

Have a good day!

Answer 4

okay.

well to begin its a inverse function you are looking for (just incase you don't know)

so with the original equation you need to make x=y and y=x so you get x = 2 ^ y

then you must change it so y is on one side

well i changed it into logarithms so log2(x) = y/f^-1(x)

so now you replace the x with 8, because its the function of 8.

Sorry i really know how to explain, but hopefully you will understand or get a better answer.

Anyway so know you have y= log2(8)

and 2 to the power of ... = 8?

well its 3 anyway.  I am unsure if you have learnt log though. Sorry if you haven't!

Answer 5

f^-1(x) is notation for the inverse function.

Starting with the original function (I'll use y instead of f(x)):

y = 2^x

Now swap the x and y variables:

x = 2^y

Now solve for y.  To do that, you would take the log base 2 of both sides:

log_2(x) = y

Reverse:

y = log_2(x)

That's your inverse function:

f^-1(x) = log_2(x)

Now plug in x = 8:

f^-1(8) = log_2(8)

Remember that log base 2 of 8 is that exponent, when raised upon the base 2 gives 8.  Because 2^3 = 8, the answer is 3.

Using logs you can solve it as follows.

= log_2(2^3)

= 3 * log_2(2)

= 3 * 1

= 3

Or with exponents:

2^y = 8

2^y = 2^3

y = 3

Answer:

3