Question

True or False?In Exercise,determine whether the statement is true or false given that f(x) = In x.if it is false,explain why or given an example that shows it is false.

if f(u) = 2f(v),then v = u2.

Answer 1

False

Explanation:

We can disprove this by plugging in u and v for f(x) = lnx

f(u) = 2f(v)

ln(u) = 2ln(v)

`ln(u) = ln(v^2)`

`u = v^2`

which is only true if u = v = 1 or 0

If u = e and v =
`e^2`

f(u) = f(e) = lne = 1

[tex]f(v) = f(e^2) = lne^2 = 2

So f(v) = 2f(u). But not the other way around