Question

WIll fan and medal please

Given the function f(x) = 0.3(4)x, what is the value of f−1(6)?

Answer 1

hard to read
is it
\[f(x)=0.3\times 4^x\]?

Answer 2

yes and the other side is the same but only -1 is an exponent 6 regular

Answer 3

lol regular 6
do you know what \(f^{-1}(x)\) means?

Answer 4

"no" is a fine answer, i am just asking

Answer 5

no I only know how to do things like f(x)-g(x) this is new

Answer 6

ok \(f^{-1}\) is the "inverse function" so if for example \(f(2)=7\) then \(f^{-1}(7)=2\)

Answer 7

more generally if \(f(x)=y\) then \(f^{-1}(y)=x\)

Answer 8

this one is a kind of hard one to solve, because what you need to do is solve
\[0.3\times 4^x=6\]for \(x\)

Answer 9

so 6-0.3 normally if normally x I'd divide the 4 next

Answer 10

first step is to divide by \(.3\) and get
\[4^x=\frac{6}{.3}=\frac{60}{3}=20\]

Answer 11

Not minus then

Answer 12

oh duh its time sorry forgot that

Answer 13

lets go slow
and i want to make sure that it is \[\huge f(x)=0.3\times 4^x\]right? the \(x\) is up in the exponent, correct?

Answer 14

yes

Answer 15

ok so we are going to solve
\[.3\times 4^x=6\] divide by \(.3\) and get
\[4^x=20\] ok with that?

Answer 16

yeah I understand that part now

Answer 17

now i am not sure what class you are taking, but you cannot use algebra to solve
\[4^x=20\] you have to use logarithms

Answer 18

are you using logs in your class? perhaps a "pre-calculus" course?

Answer 19

4x=20 = x = ln (20) over ln (4)

Answer 20

got it

Answer 21

= 2.1 right?

Answer 22

thank you very much! It's much easier explained out now

Answer 23

looks good
http://www.wolframalpha.com/input/?i=ln%2820%29%2Fln%284%29
but if you want to round, use \(2.2\) or \(2.16\)

Answer 24

yw