Question

Some function and domain questions, attachments below

Answer 1

• f(x+3) = 4x + 12, you can factorize 4x + 12 like this:
$f(x + 3) = 4(x + 3)$
Like this you can replace x+3 for and you will get the formula you need for f(x):
$f(x) = 4x$

•
$\sqrt{x + 4} - \sqrt{x - 9}$
since the radicand can only be 0 or a positive number, x+4 and x-9 must both be 0 or positive

$x + 4 \geqslant 0 \\ x \geqslant - 4$
and
$x - 9 \geqslant 0 \\ x \geqslant 9$
with this we know that x has to be:
$x \geqslant 9$
and the domain is: [9,∞)