What's f^-1(7)?

Question

If f(x)=2^x+1, then what does f^-1(7)=?

Answer 1

If f is a one-to-one function and if f(a) = b, then f^-1(b) = a.

 

So, we need to find "a" so that f(a) = 7

 

                                         2^a+1 = 7

 

                                             2^a = 6

 

                                          ln(2^a) = ln6

 

                                        a(ln2) = ln6

 

                                               a = ln6/ln2

 

Answer 2

Diana,

   

That question is the same as asking "What value of x gives you an output of 7 ?"

 

So, set 7 equal to f(x) and solve for x:

     7 = 2^x + 1

     6 = 2^x              (subtracted 1 from both sides)

  ln(6) = x ln(2)   (think "log" when x is in the exponent)

  ln(6)/ln(2) = x   (divided both sides by ln(2))

 

        x = 2.58496   

 

 

Check:  2^2.58496 + 1 = 6 + 1 = 7  (ok)