Given: g(x)= sqrt x-4 and h(x)=2x-8 . what are the restrictions on the domain of g*h?

Given : g(x) =  and h(x)=2x-8.

Let us find g*h(x) function now.

g*h(x) = g(x) * h(x) =

Or g*h(x) =(2x-8).

He have square root(x-4) in composite function f*h(x).

So, we need to find the domain, we need to check for that values of x's, square root(x-4) would be defined.

Square roots are undefined for negative values.

Therefore, we can setup an inequality for it's domain x-4≥0.

Adding 4 on both sides, we get

x-4+4≥0+4.

x≥4.

Therefore, Domain is all values greater than or equal to 4.

But, restrictions would be all values less than 4 (because less than 4 would give a negative number inside square root).

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.

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: