Let's work through another example together. Problem Given f(x) = x + 3x 3 and g(x)...

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Let's work through another example together. Problem Given f(x) = x + 3x 3 and g(x) = 2x, find f(g(x)). Solution First, we need to decide which function will go inside which. Since our function reads "f of g of a", we know that we are going to substitute the function for g(x) into every a spot in the f(x) function. f(g(x)) =( +3( -3 Next, perform normal order of operations for each term. (Hint: (2x)2 = (2x) (2x)) f(g(x)) = x+ 3 Let's look at how this example would be different if it was performed in the opposite order. Given f(x) = x + 3x - 3 and g(x) = 2x, find g(f(x)). In this case, we'll need to plug the whole function for f(x) into the input (x) spot in the g(x) function. g(f(x)) = (x + 3x - 3) Then we'll distribute to each term. g(f(x)) =2 (x)+ Simplify to get the final answer. g(f(x)) = x+ Check Composition of Functions Interactive (3x) - x 6 3 Let's work through another example together. Problem Given f(x) = x + 3x 3 and g(x) = 2x, find f(g(x)). Solution First, we need to decide which function will go inside which. Since our function reads "f of g of a", we know that we are going to substitute the function for g(x) into every a spot in the f(x) function. f(g(x)) =( +3( -3 Next, perform normal order of operations for each term. (Hint: (2x)2 = (2x) (2x)) f(g(x)) = x+ 3 Let's look at how this example would be different if it was performed in the opposite order. Given f(x) = x + 3x - 3 and g(x) = 2x, find g(f(x)). In this case, we'll need to plug the whole function for f(x) into the input (x) spot in the g(x) function. g(f(x)) = (x + 3x - 3) Then we'll distribute to each term. g(f(x)) =2 (x)+ Simplify to get the final answer. g(f(x)) = x+ Check Composition of Functions Interactive (3x) - x 6 3

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