Find f(g(x)). State the domain of the composite function.
f(x) = 3x-2/x+1
g(x) = x+5/2x-3

ℝ - {(-2/3),(3/2)}

Step-by-step explanation:

We want the domain of f(g(x)). So, firstly, we have to find the domain for g(x) and, then, for f(g(x)).

- Domain of g(x): Since the expression is a fracion, we must exclude the values of x that make null the denominator. Hence,

- Domain of f(g(x)): We'll find its expression:

Now, once again, we have to exclude the values of x that make the denominator equals to zero. Thus,

Lastly, we may write the domanin of f(g(x)):

or, just writing in a shorter way:

step-by-step explanation:

i hate black

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation: