The Nature of Functions

If f(x)= (x-6)/x, g(x)= x+4, and h(x)= 3x-2, what is (h*f*g)(x)?

(h*f*g)(x)= (x-14)/(x+4)

If r(x)= 2-x^2 and w(x)= x-2, what is the range of (w*r)(x)?

(∞,0]

if k(x)= 5x-6, which expression is equivalent to (k+k)(4)?

5(4)-6+5(4)-6

If f(x)= 3x^2 and g(x)= 4x^3+1, what is the degree of (f*g)(x)?

6

how is the graph of y=\root(3)(x-4) transformed to produce the graph of y=-\root(3)(2x-4)

The graph is compressed horizontally by a factor of 2, moved left 4 units, and moved down 4 units.

If (f)= x^2-25 and g(x)= x-5, what is the domain of (f/g)(x)?

all real values of x except x= 5

let f(x)= |x| and g(x)= x+2. What are the domain and range of (f*g)(x)?

domain: all real numbers range: y>= 0

which statement verifies that f(x) and g(x) are inverses of each other?

f(g(x))= x and g(f(x))= x

Which function is the inverse of f(x)= -5x-4

f^1(x)= -1/5x-4/5

If the function f(x)= mx+b has an inverse function, which statement must be true?

m =/ 0

let f(x)= 4^x and g(x)= x+3. The graph (f*g) is shown below.

y>0