State the domain restriction(s) in interval notation of \displaystyle f\left(g\left(x\right)\right)f(g(x) ) given: \displaystyle f\left(x\right)=\sqrt{3x-2}f(x)= 3x−2 and \displaystyle g\left(x\right)=x-7g(x)=x−7

The interval notation for the domain is .

Step-by-step explanation:

Consider the provided information.

It is given that

We need to find the value of .

Put the value of g(x) in  .

 ....(1)

Now, put x=x-7 in

From equation 1.

The domain of the function is the set of input values for which a function is defined.

Here, the value of should be greater or equal to 0 as the square root of a negative number is not real.

Domain=

The value of x is all real number greater than .

Hence, the interval notation for the domain is .

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

quit

step-by-step explanation: