Question

Determine the domain

Answer 1

\[(h o g)(x)\]
\[h(x)=\frac{ 1+2x }{ 1-2x }\]
\[g(x)=\sqrt{1-2x}\]

Answer 2

first frite the expretion for hog(x)

Answer 3

\[hog(x)=\frac{1+2\sqrt{1-2x}}{1-2\sqrt{1-2x}}\]

Answer 4

then

Answer 5

now, there will be to evident conditions for this expretion to have any meaning:
1-2x>0
and
1-2sqrt(1-2x) not equal to 0

Answer 6

and

Answer 7

for the first one:
1>2x it means x<1/2
for the 2º one:
1-2sqrt(1-2x)=0
1=2sqrt(1-2x)
1/2=sqrt(1-2x)
1/4=1-2x
2x=1-1/4=3/4
x=3/8 this value of x will make it 0, so need to be excluded from domain.
Now just combine bouth conditions:
x<1/2 and x not equal to 3/8

Answer 8

@AravindG please help me with this

Answer 9

it gives me the domain (-inf, 1/2) but i don't know how he come up with that

Answer 10

in first equation for h(x) to be defined 1-2x should not be equal to 0

Answer 11

find the value of x for which this happens and remove it from the domain

Answer 12

why?

Answer 13

because a fraction is not defined with denominator=0

Answer 14

oh that's how he got the 1/2

Answer 15

and then