Ordering Composite Function Values
Define the following functions:
• f(x) = $$x^2$$
• g(x) = $$2*x + 1$$
• h(x) = $$\sqrt{x + 4}$$
• k(x) = $$\ln(x + 5)$$
Evaluate the composite function values at x = 3 as follows:
• f(g(3)): g(3) = 2*3 + 1 = 7, so f(g(3)) = 49
• f(h(3)): h(3) = $$\sqrt{7}$$ so f(h(3)) = 7
• f(k(3)): k(3) = $$\ln(8)$$ $$\approx 2.08$$, so f(k(3)) $$\approx (2.08)^2 \approx 4.32$$
• f(3) = 9
Rank these values from smallest to largest.
A
f(k(3)), f(h(3)), f(3), f(g(3))
B
f(3), f(k(3)), f(h(3)), f(g(3))
C
f(k(3)), f(3), f(h(3)), f(g(3))
D
f(h(3)), f(k(3)), f(3), f(g(3))
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