Answer to Question #329382 in Functional Analysis for Ankush Kumar

Question

Say True or False with proof

Q1. If 𝑓(𝑥) = 2|𝑥 − 1| and 𝑔(𝑥) = 3𝑥 − 10,

then 𝑓𝑜𝑔(1) = 12.

Q2. (√2, 1,1/2)∈ 𝑸 × 𝒁 × 𝑹.

Q3. The domain of the function f defined by 𝑓(𝑥)

=√{(3-x)/(x-2)} is R-{2}.

Answer 1

Q1 false

$f\circ g= 2|3x-10-1|=2|3x-11|$

$f\circ g(1)=2|3\cdot 1-11|=16$

Q2 false

$\sqrt 2\notin Q,1\isin Z,1/2\isin R$

Q3 false

$f(x)=\sqrt{(3-x)/(x-2)}$

domain: $x\isin (2,3]$