How do you find the inverse of #f(x) = 200*3^(x/4) #?
1 Answer
Apr 7, 2018
See below
Explanation:
Given:
- Switch the x and the y:
#x= 200*3^(y/4)# - Solve for y by dividing by 200:
#x/200=3^(y/4)# - Apply logarithm:
#log_3(x/200)= y/4# - Multiply by 4 on both sides:
#4log_3(x/200)= y# -
Write with inverse notation:
#f^(-1)(x)=4log_3(x/200) # -
Symmetric across
#y=x# check:
graph{200*3^(x/4) [-71.4, 102.55, -11.7, 75.25]} graph{y=x [-62.74, 111.2, -64.9, 22.06]}
graph{4((log(x/200))/log3) [-62.74, 111.2, -64.9, 22.06]}