SOLUTION: A) given : f(x) = 3^x find f^-1 (x) B) given : g(x)=log 3x find g^-1(x)

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Question 1079777: A) given : f(x) = 3^x find f^-1 (x)
B) given : g(x)=log 3x find g^-1(x)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
A)
given :
f%28x%29+=+3%5Ex find f%5E-1+%28x%29
note: f%28x%29+=y
y+=+3%5Ex..........swap x and y
x+=+3%5Ey..........solve for y
log%28x+%29=+log%283%5Ey%29
log%28x+%29=+y%2Alog%283%29
y=log%28x+%29%2Flog%283%29
so, f%5E-1+%28x%29=log%28x+%29%2Flog%283%29


B)
given :
+g%28x%29=log%28+3x%29 find g%5E-1%28x%29+
y=log%28+3x%29
x=log%28+3y%29
x=log%28+3y%29
x%2A1=log%28+3%29%2Blog%28y%29............1=log%2810%2C10%29
x%2Alog%2810%2C10%29=log%28+3%29%2Blog%28y%29
log%2810%2C10%5Ex%29-log%28+3%29=log%28y%29
log%2810%2C10%5Ex%2F+3%29=log%28y%29
10%5Ex%2F+3=y
so, g%5E-1%28x%29=10%5Ex%2F3