3. Evaluate the indicated function for f(x) = x2 − 1 and g(x) = x − 8 algebraically. If possible, use a graphing utility to verify your answer. (f − g)(-8)
4. Evaluate the indicated function for
f(x) = x2 − 5 and g(x) = x − 7 algebraically. If possible, use a graphing utility to verify your answer. (f + g)(1)
5. Evaluate the indicated function for f(x) = x2 − 1 and g(x) = x − 10 algebraically. If possible, use a graphing utility to verify your answer. (f/g)(0).
7. Given f(x) = x2 + 4 and (fg)(x) = 6x(x2 + 4), what is g(x)?
10. Given (f ∘ g)(x) = f(x2 + 6), what is g(x)?
12. Consider the functions below.
f(x)=x3
g(x)=1/x
(a) f∘g=
(b)g∘f=
(c)(f∘g)(0)=
14. A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius (in feet) of the outermost ripple is given by
r(t) = 0.3t,
where t is time (in seconds) after the pebble strikes the water. The area of the circle is given by
A(r) = 𝜋r2.
Find (A ∘ r)(t).