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Composite function and characteristics of a graph

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1. Given f(x) = 4x^2 - 3 and g(x) = 5 - 1/2x^2. Find the following expressions. Simplify your answer for all solutions.
(a) (f o g)(4)
(b) (g o f)(2)
(c) (f o f)(1)
(d) (g o g)(0)

2. For the given equation, list the intercepts and test for symmetry. x^2 + y - 16 = 0
A. What are the intercept(s)? Write as an ordered pair or there are no intercepts.
B. Is the graph of the equation symmetric with respect to the x-axis?
Is the graph of the equation symmetric with respect to the y-axis?
Is the graph of the equation symmetric with respect to the origin?

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Solution Summary

In this solution, composite function values and characteristics of a graph for a given function are estimated.

Solution Preview

F(x) = 4x^2 - 3
g(x) = 5 - x^2/2

Fog(4) = F(g(4)) = F(5 - 4^2/2) = F(5 - 8) = F(-3) = 4*(-3)^2 - 3 = 33

goF(2) ...

Solution provided by:
  • BEng, Allahabad University, India
  • MSc , Pune University, India
  • PhD (IP), Pune University, India
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