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Composite Functions

Problem of finding out fog and gof can also be handled using graphical methods

f(g(x))    equation-for-fog

               finding-out-fog-and-gof                  

Here g(x) becomes the variable that means we would draw the graph of g(x). It is clear that g(x) < 1 ∀ x ε [-1, 1] and 1 < g(x) < 2 ∀ x ε (1, √2]

equation-for-gof

                                  the-graph-of-f(x)

In this case f(x) becomes the variable and we will draw the graph of f(x). From the graph we observe that -1 < f(x) < 2 ∀ x ε [-2, 1) and f(x) = x + 1.

2 < f(x)) < 3 => x = 1 and f(x) = x + 1.

draw-the-graph-of-f(x)

i.e. g(f(x)) = (x + 1)2, -2 < x < 1

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