SOLUTION: Hello. I have to find the f[g(x)] for the functions f(x)=4x+9;g(x)=-5x+7. could you please send me the step by step solution so I can learn it the right way. thank you and have

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Question 624932: Hello. I have to find the f[g(x)] for the functions f(x)=4x+9;g(x)=-5x+7. could you please send me the step by step solution so I can learn it the right way. thank you and have a good day
Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!
Problems like this are alot easier once you learn to understand what something like:
f(x) = 4x + 9
is telling you. The expression inside the parentheses following a function name is the input to the function. The "x" here is simply a place-holder for whatever input you choose to put into function f. The right side of the equation tells us what this particular function f will do with its input. It tells us that f will take the input, multiply it by 4 and then add 9. It will do this for any input to f, not just an input of x. In summary, f(x) = 4x + 9 tells us that f will multiply any input by 4 and then add 9.

Once we get this idea, it is a lot easier to see how to handle:
f(g(x))
which says that g(x) is the input being put into function f. And what does f do with any input? It multiplies it by 4 and adds 9! So
f(g(x) = 4(g(x)) + 9
Since g(x) = -5x + 7 this becomes:
f(g(x)) = 4(-5x + 7) + 9
which simplifies as follows:
f(g(x)) = -20x + 28 + 9
f(g(x)) = -20x + 37

Some other examples:
f(q) = 4q+9
f(2x) = 4(2x) + 9 = 8x + 9

f(x+6) = 4(x+6) + 9 = 4x + 24 + 9 = 4x + 33
etc.