Verified answer

g(f(x))=3(√5x)-2

Hope this helps!

f and g are "recipes"

f(x) and g(x) give you the instructions on how to use the ingredient (x) in each recipe.

If you are told g(x) = 3x - 2, then whatever you are given for the ingredient x, will be used everywhere the recipe tells you to use x.

for example, you are asked to solve for x = 17, you will write

g(17) = 3(17) - 2 = 51 - 2 = 49

Here, you are asked to use "f(x)" (which happens to be another recipe).

so, you follow the instructions:

g(f(x)) = 3(f(x)) - 2

Since you are told that f(x) = √5x

you can use that

g(f(x)) = 3(√5x) -2

This is a case where you need to follow one recipe inside another.

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The same idea does exist in cooking, where one recipe (say a Moussaka) may ask you to add a Béchamel sauce on top of the tomatoes, before cooking. This would force you to follow another recipe (sauce) in order to complete your original recipe (the moussaka).

g(f(x))=3(√5x) - 2, you only change the x from g(x) with √5x

if you would have f(g(x)) =?

f(g(x))=√5(3x-2)

g ( f (x) ) = g ( √5 x ) = 3√5 x - 2