Find the inverse of fx X 4x Find the domain of fx log x2

Find the inverse of f(x) = X + 4/x Find the domain of f(x) = log (x^2 - 9) Find the domain of (f log)(x) if f(x) = squarerootx-1, g(x) = 1/X-5 Express as a single logarithm i/2 logx - 1/3 log_2 (x + y) - log w solve for X log (X-3) = 1 - logx 3^x+10 = 4^x e^2x + 2e^x + 1 = 0 f(x) 1 + log(x-2) Find the domain Write the equation Find x-y-Integer Graph f(x) statement has found a greet must she has found a way to receive a final interest rate of 12% compound If she has $600 to now a to end up with $1000.

Solution

1) inverse of f(x)= (x+4)/x

to find the inverse,first we write y in place of f(x) and then switch y and x

y=(x+4)/x

x=(y+4)/y

Next is to solve for y

x=1 + 4/y

x-1=4/y

y=4/x-1

f^-1(x)=4/(x-1)

2) f(x)=log(x^2 - 9)

log cant take 0 or negative values.

Therefore x^2-9>0

(x+3)(x-3)>0

on solving we get

x<-3 and x>3

Therefore the domain is (-infinity,-3)U(3,infinity)