Given the function f(x) = 0.5(3)^x, what is the value of f−1(7)?

Question

isaiah.feynman · Answer

First find the inverse.

jdoe0001 · Answer

$\bf f(x) = y= 0.5(3)^x\qquad inverse\implies x= 0.5(3)^y$

solve for "y"

anonymous · Answer

i have no idea how to do this i need some explaining :(

jdoe0001 · Answer

notice, all you do is swap the variables about, to get the inverse

anonymous · Answer

oh okay i understand

anonymous · Answer

what do i need to do now? @jdoe0001

anonymous · Answer

so now i have x= 0.5(3)^y how do i find the value of f^−1(7)?

jdoe0001 · Answer

hmm... have you cover logarithms yet?

anonymous · Answer

no, just exponential functions..

jdoe0001 · Answer

hmm... well.... then maybe that's all, you leave it as exponential
because to solve for "y", it'd end up as a logarithmic function

anonymous · Answer

okay, thats it?

jdoe0001 · Answer

I'd think so, yes :)

anonymous · Answer

that not one of the options :/

anonymous · Answer

Given the function f(x) = 0.5(3)x, what is the value of f−1(7)?
0.565
1.140
1.771
2.402

jdoe0001 · Answer

hmmm   so what are your choices?

jdoe0001 · Answer

ohhh... wait.. your options will be just a value... however... to get that value, you'd need the logarithmic function, which you haven't covered

anonymous · Answer

okay thanks :) ill try and figure it out