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.

(f(x))1/2 = 1/2f(x)

Answer 1

False.

Explanation:

Data provided in the question:

f(x) = In x

To check:
`(f(x))^{(1)/(2)} = (1)/(2)*\ f(x)`

now,

substituting the function in the given relation

`(\ln(x))^{(1)/(2)} = (1)/(2)*\ln(x)`

also, we know

log(aᵇ) = b × log(a)

therefore,

`(\ln(x))^{(1)/(2)}` ≠
`\ln(x^{(1)/(2)})`

here,

LHS is not equal to RHS

Hence,

The given relation in the question is False.