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`

•

`√(x + 4) - √(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,∞)