Let h R rightarrow R be defined by hx 3x 2 and g R rightar

Let h: R rightarrow R be defined by h(x) = 3x + 2 and g: R rightarrow R be defined by g(x) = x^3. Determine formulas lor the composite functions g o h and h o g. Is the function g o h equal to the function h o g? Explain. What does this tell you about the operation of composition of functions?

Solution

h and g are two functions defined from R to R

h(x) = 3x+2 and

g(x) = x³

For composition of function fog (x) we first apply g to x and then apply f to the result.

i.e. hog (x) = h{g(x)} = h(x^3)

= 3x³+2

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For goh (x) = g{h(x)} = g(3x+2)

= (3x+2)³

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Thus hog is not equal to goh,

In other words, composition of functions is not commutative and so we cannot change the order.