Question

Given the function f(x) = 0.3(4)^x, what is the value of f^−1(6)?
a: 0.360
b:1.242
c:2.161
d:2.312

Answer 1

to find the inverse "relation" you'd simply swap about the variables, so

\(\bf f(x) ={\color{red}{ y}} =0.3(4)^{\color{blue}{ x}}\qquad inverse\implies {\color{blue}{ x}}=0.3(4)^{\color{red}{ y}}
\\ \quad \\
\textit{log cancellation rule of }{\color{blue}{ log_aa^x=x}}\qquad thus
\\ \quad \\
{\color{blue}{ x}}=0.3(4)^{\color{red}{ y}}\implies \cfrac{x}{0.3}=4^y\implies log_4\left(\cfrac{x}{0.3}\right)=log_4(4^y)
\\ \quad \\

log_4\left(\cfrac{x}{0.3}\right)=y \iff f^{-1}
\\ \quad \\
f^{-1}(16)=log_4\left(\cfrac{16}{0.3}\right)\)

Answer 2

hmm 6

Answer 3

\(\bf f^{-1}(6)=log_4\left(\cfrac{6}{0.3}\right)\)

Answer 4

So, would that be a?

Answer 5

@jdoe0001