Question 305452
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Any time you are given *[tex \Large f(x)] (or *[tex \Large g(x)] or *[tex \Large h(x)] or *[tex \Large \phi(x)] for that matter) and a definition of the function as an expression involving *[tex \Large x], then you need to read it as "the value of the function *[tex \Large f] at *[tex \Large x] is: "


So if the value of the function *[tex \Large f] at *[tex \Large x] is *[tex \Large 3x^2\ -\ 11x], then the value of the function *[tex \Large f] at *[tex \Large 0] is *[tex \Large 3(0)^2\ -\ 11(0)\ =\ 0].


Whatever is in the parentheses replaces *[tex \Large x] in the function definition -- then do the appropriate arithmetic.


Also:


If *[tex \Large f(x)\ =\ 3x^2\ -\ 11x], then  *[tex \Large f(a)\ =\ 3a^2\ -\ 11a], or *[tex \Large f(x+h)\ =\ 3(x+h)^2\ -\ 11(x+h)], or, if *[tex \Large g(x)\ =\ x^2\ -\ 3], then *[tex \Large f(g(x))\ =\ 3(g(x))^2\ -\ 11(g(x))\ =\ 3(x^2-3)^2\ -\ 11(x^2-3)]


Your other problem says that the value of the function at *[tex \Large x] is 83 no matter what the value of *[tex \Large x] might be.  So, *[tex \Large f(x)\ =\ 83] means that *[tex \Large f(0)\ =\ 83], *[tex \Large f(-16)\ =\ 83], and *[tex \Large f(125,486,557,855,965,332,545,872,263,331,145,532,556,774)\ =\ 83]



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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