Explore BrainMass
Share

Explore BrainMass

    Composite function and characteristics of a graph

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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?

    © BrainMass Inc. brainmass.com October 10, 2019, 7:49 am ad1c9bdddf
    https://brainmass.com/math/basic-algebra/composite-function-characteristics-graph-596613

    Attachments

    Solution Preview

    1.
    F(x) = 4x^2 - 3
    g(x) = 5 - x^2/2

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

    b.
    goF(2) ...

    Solution Summary

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

    $2.19