1. Find Range and Domain!?!?!?!?

ok i dont actually know how to find the range and domain of a function so could anyone please show me how, and also this is my question that needs answering please.

f:x = 2x + ln2
g:x = e^(2x)

gf:x = 4e^(4x), (x E R)

the question asks to find the range of gf.

Part (c) is write down the range and domain of: ln(4-2x)

2. Originally Posted by Stylis10
ok i dont actually know how to find the range and domain of a function so could anyone please show me how, and also this is my question that needs answering please.

f:x = 2x + ln2
g:x = e^(2x)

gf:x = 4e^(4x), (x E R)

the question asks to find the range of gf.
The range of $\displaystyle 4e^{4x}$ is $\displaystyle (0,\infty)$. The range is essentially the range of $\displaystyle e^t$ and we know that e^t is always positive.

Part (c) is write down the range and domain of: ln(4-2x)
$\displaystyle \ln y$ is defined only when $\displaystyle y > 0$, using this we can say the domain is $\displaystyle 4 - 2x > 0 \Rightarrow x < 2$. Thus the range is $\displaystyle \mathbb{R}$.

3. Originally Posted by Isomorphism
The range of $\displaystyle 4e^{4x}$ is $\displaystyle (0,\infty)$. The range is essentially the range of $\displaystyle e^t$ and we know that e^t is always positive.

$\displaystyle \ln y$ is defined only when $\displaystyle y > 0$, using this we can say the domain is $\displaystyle 4 - 2x > 0 \Rightarrow x < 2$. Thus the range is $\displaystyle \mathbb{R}$.

thans that helped alot