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# composite fuctions

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https://vle.mathswatch.co.uk/images/questions/question2233.png

need help quick plz

lynx7  Feb 10, 2018

#1
+6365
+2

a)   This must mean find  f( g(x) ) .

f(x)   =   2x - 3

f( g(x) )   =   2( g(x) ) - 3

And  g(x)  =  x2 + 1 , so we can replace  g(x)  with  x2 + 1 .

f( g(x) )   =   2(x2 + 1) - 3

f( g(x) )   =   2x2 + 2 - 3

f( g(x) )   =   2x2 - 1

b)   Find  g( f(x) ) .

g(x)   =   x2 + 1

g( f(x) )   =   ( f(x) )2 + 1

And  f(x)  =  2x - 3 , so we can replace  f(x)  with  2x - 3 .

g( f(x) )   =   (2x - 3)2 + 1

g( f(x) )   =   (2x - 3)(2x - 3) + 1

g( f(x) )   =   4x2 - 12x + 9 + 1

g( f(x) )   =   4x2 - 12x + 10

hectictar  Feb 10, 2018
Sort:

#1
+6365
+2

a)   This must mean find  f( g(x) ) .

f(x)   =   2x - 3

f( g(x) )   =   2( g(x) ) - 3

And  g(x)  =  x2 + 1 , so we can replace  g(x)  with  x2 + 1 .

f( g(x) )   =   2(x2 + 1) - 3

f( g(x) )   =   2x2 + 2 - 3

f( g(x) )   =   2x2 - 1

b)   Find  g( f(x) ) .

g(x)   =   x2 + 1

g( f(x) )   =   ( f(x) )2 + 1

And  f(x)  =  2x - 3 , so we can replace  f(x)  with  2x - 3 .

g( f(x) )   =   (2x - 3)2 + 1

g( f(x) )   =   (2x - 3)(2x - 3) + 1

g( f(x) )   =   4x2 - 12x + 9 + 1

g( f(x) )   =   4x2 - 12x + 10

hectictar  Feb 10, 2018

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