# Math forum

 Composite Functions Options
burgess.raq
 #1 Posted : Tuesday, July 26, 2011 1:33:59 AM
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Given that f(x)=2x^2 -x+1, g(x)=2sinx  and h(x)=3^x, determine the following:

a) f(g(x))

b)h^-1(f(x))

c) g(f(h(x)))

thanks!

HollyCeci
 #2 Posted : Friday, September 02, 2011 1:22:55 PM
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"Given that f(x)=2x^2 -x+1, g(x)=2sinx  and h(x)=3^x, determine the following:

a) f(g(x))

b)h^-1(f(x))

c) g(f(h(x)))"

f(g(x)) means that g(x) is the new "variable" for the function f.

For example,

if f(x) = 2x + 1

and I want to find f(y), then I just replace all the x's in the f(x) function with y's so the result is

f(y) = 2y + 1.

If I have a second function of

g(x) = 4x^2 - 9x

and I want to find f(g(x)), then all of the x's in f will be replaced with the entire function g.  I think of the function f as 2 times "something" plus one.  I then write the function f without the x and leave a blank like so,

f(x) = 2(_____) + 1.

I then fill in the blank with the g funciton.  The result will be

f(g(x)) = 2(4x^2 - 9x) + 1.

You can do the same with part a, just be mindful that you have more than one x.  Each x needs to be replaced with the function g(x).

For part b, now you are dealing with inverse functions.  An inverse function switches the inputs (domain) and outputs (range) of the original function and will be symmetric across the line y = x when graphed.  The inverse of an exponential function is a logarithm.

For example, if

h(x) = 2^x

then

h^-1(x) = log (base 2) of x

For part c of your question, you will first need to find f(h(x)) like you did for part a, and then take that new function and replace all of the x's in g with it.

I hope that this helps!

aljazari
 #3 Posted : Tuesday, May 29, 2012 9:09:19 PM
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