Question 343026: Function composition: f(x)=4x-3, g(x)=5xsquared-2 and i need the to have the g[f(X)] explained. Thanks!
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
If you have a function  such that the value of the function at  , namely ) is defined by some expression involving , then you evaluate ) by replacing in the definition of with a  and then doing the arithmetic.
Just as an example, let's define \ =\ x^2\ +\ 2x\ - 3) . Given that definition, \ =\ (1)^2\ + 2(1)\ - 3) , whereas \ =\ (2)^2\ + 2(2)\ - 3) . Of course, you need to do the arithmetic and simplify, but the concept is simply that you replace the independent variable by whatever is in the parentheses following the function identifier.
Therefore, if someone says, evaluate ) where , you replace the variable with  , thus:
\ =\ a^2\ +\ 2a\ - 3) .
And the same idea to evaluate ) which would look like:
\ =\ \left(\frac{-b}{2a}\right)^2\ +\ 2\left(\frac{-b}{2a}\right)\ - 3) .
So you need to write out your ) and then replace the independent variable, , with the definition of ) . And then simplify, of course.
John
My calculator said it, I believe it, that settles it
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