(8) Let f(x)=3x^2-5 and g(x)=sqrt(x-1).

(a) Find  (f of g)(x).

  1. First plug in the g(x) equation in the x of the f(x) equation.

=4(sqrt(x-1))^2-2

2. The next step is to square the square root.

=4(x-1)-2

3. After you distribute the 4 to the x and one.

=4x-4-2

4. Then add the like terms.

=4x-6

(b)Determine the domain of (f of g)(x)

  1. Get rid of the square root of the function and make it equal to 0

= X-1=0

2. Add 1 to the other side to isolate x

=x=1

3. After replace the equal sign with a greater than equal sign

=x is greater than or equal to 1

4. Write the answer in interval notation

Domain=[1, Inf)