Question

Find a formula for f(x) an exponential function such that f(2)= 1/126 and f(-1)=126

Answer 1

Explanation:

Since 8 is a power of 2

`\boxed{f(x)=k*2^(ax)}\\\\f(2)=k*2^(2a)\\f(-1)=k*2^(-a)\\\\(f(2))/(f(-1)) =(k*2^(2a))/(k*2^(-a)) =(1)/(8*8) \\\\2^(3a)=2^(-6)\\\\a=-2\\\\f(2)=k*2^(2a) \ \Longrightarrow\ k*2^(-4)=2^(-3)\\k=2\\\\\boxed{f(x)=2*2^(-2*x) =2^(-2x+1) }\\`