# Composite function and characteristics of a graph

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?

https://brainmass.com/math/basic-algebra/composite-function-characteristics-graph-596613

#### 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.