Question

Hi I don't understand how to go about this question. thanks in advance for help.
The domains of these functions are the set of all positive real numbers, Find their ranges,
1. f(x)=2x+7
2. f(x)=x^2-1

Answer 1

@nincompoop

Answer 2

the domain is all the possible x values which in this case is x>0
the range is all the possible y values

Answer 3

Note: number 2 - what sign is a square number?

Answer 4

- if x is real can a square number ever be negative?

Answer 5

In any case x>0 as alekos has said so what does that make the range of values of x^2?

Answer 6

\[x>0 \rightarrow 2x >0 \rightarrow 2x+7 >0+7\\x> 0 \rightarrow x^2 >0 \rightarrow x^2-1>0-1\]

Answer 7

Nice answer amoodarya

Answer 8

Sorry I was afk, thanks to all for answering

Answer 9

@amoodarya how do I apply this to one of the later questions: f(x) = (x+2)^2-1

Answer 10

for f(x)=2x+7
if x>0
then f(x) will be bigger than 7
the range is y>7

Answer 11

with f(x) = (x+2)^2 -1
just apply the same procedure

x>0
x+2>2
and so on until you get f(x) > ......