need help with algebra?

Question

1.)
is this a linear function? solve for y...
4y^-1=(-5x^-1)+5

2.)
what is the inverse function of the following:
f(x)=2-3 4log(x+1)

Answer 1

To answer the first question, you need to solve for Y first and THEN see if it is linear.

if 4/y = -5/x + 5
multiply both sides by y, and get
4/(-5/x+5) = y
This definitely is NOT linear

2) if f(x) = 2-34log(x+1) then
(f(x)-1)/34 = log(x+1)
and exp((f(x) - 1)/34) = x+1
so x = exp((f(x)-1)/34) - 1

Answer 2

1. Yes it's linear.
Rewrite as: (4/y)=(-5/x)+5
Multiply through with y: 4=y[(-5/x)+5]
Isolate y: y=4/[(-5/x)+5]
Simplify: y=(4/-5)x+(4/5)

2. I know the inverse function of log functions is exponential functions, but that's all.

Answer 3

4y^-1 = (-5x^-1) + 5
4/y = (-5/x) + 5
4/y = (-5 + 5x)/x
y/4 = x/(-5 + 5x)
y = (4x)/(-5 + 5x)
y = (-4/5)(x/(1 - x))
y = (-4/5)(x/(-x + 1))
y = (-4/5)(x/(-(x - 1)))
y = (4/5)(x/(x - 1))
y = (4x)/(5x - 5)

This isn't a Linear Function

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