• f(x+3) = 4x + 12, you can factorize 4x + 12 like this:
[tex]f(x + 3) = 4(x + 3)[/tex]
Like this you can replace x+3 for and you will get the formula you need for f(x):
[tex]f(x) = 4x[/tex]
•
[tex] \sqrt{x + 4} - \sqrt{x - 9} [/tex]
since the radicand can only be 0 or a positive number, x+4 and x-9 must both be 0 or positive
[tex]x + 4 \geqslant 0 \\ x \geqslant - 4[/tex]
and
[tex]x - 9 \geqslant 0 \\ x \geqslant 9[/tex]
with this we know that x has to be:
[tex]x \geqslant 9 \\ [/tex]
and the domain is: [9,∞)
