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Given ƒ(x) = x2 + 4 and g(x) = 5x − 3, find (ƒ ○ ƒ)(x).

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Given ƒ(x) = x2 + 4 and g(x) = 5x − 3, find (ƒ ○ ƒ)(x).

asked May 26, 2014 in PRECALCULUS by bilqis Pupil

1 Answer

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The functions f (x ) = x 2 + 4 and g (x ) = 5x - 3

(f of )(x ) = f (f (x ))

Substitute the expression for functioning f  (in this case x 2 + 4 ) for f (x ) in the composition.

= f (x 2 + 4)

Now substitute this expression (x 2 + 4) in to function in place of the x  value.

= (x 2 + 4)2 + 4

(a + b )2 = a 2 + b 2 + 2ab

a = x 2  and b = 4

= x 4 + 16 + 8x 2 + 4

= x 4 + 8x 2 + 20

(f of )(x ) = x 4 + 8x 2 + 20.

answered May 26, 2014 by david Expert

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