Composition of Functions

If f(x) = x^2 + 1 and g(x) = x - 4, which value is equivalent to (f*g)(10)?

a. 37

If h(x) = x - 7 and g(x) = x^2, which expression is equivalent to (g*h)(5)?

(5 - 7)^2

If h(x) = 5 + x and k(x) = 1/x, which expression is equivalent to (k*h)(x)?

b. 1/(5 + x)

If s(x) = x - 7 and t(x) = 4x^2 - x + 3, which expression is equivalent to (t*s)(x)?

b. 4(x - 7)^2 - (x - 7) + 3

If h(x) = 6 - x, what is the value of (h*h)(10)?

c. 10

Which description best explains the domain of (g*f)(x)?

a. the elements in the domain of f(x) for which g(f(x)) is defined

If u(x)= -2x^2 + 3 and v(x)= 1/x, what is the range of (u*v)(x)?

c. (-∞, 3)

If p(x) = 2x^2 - 4x and q(x) = x - 3, what is (p*q)(x)?

c. 2x^2- 16x + 30

If f(x) = 3x + 2 and g(x) = x^2 + 1, which expression is equivalent to (f*g)(x)?

d. 3(x^2 + 1) + 2

The domain of f(x) is the set of all real values except 7, and the domain of g(x) is the set of all real values except -3. Which of the following describes the domain of (g*f)(x)?

d. all real values except x = 7 and the x for which f(x) = -3