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Composition of Functions - Please Help!










































I cannot figure out this problem...can you please help?

if f(x)=x^2+3x-1 and g(x)=x63-3x+2, then f(g(-1))=?

a) -16
b) -12
c) -3
d) 4
e) 27

thank you
Thomas

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Mar 12, 2012
Composition of Functions – Evaluate at a Point
by: Staff


Question:

I cannot figure out this problem...can you please help?

if f(x) = x^2 + 3x - 1 and g(x) = x^63 - 3x + 2, then f(g(-1)) = ?

a) -16
b) -12
c) -3
d) 4
e) 27

thank you
Thomas


Answer:


g(x) = x^63 - 3x + 2

. . . . g(-1) means you should substitute -1 for every x in the equation

g(-1) = (-1)^63 - 3*(-1) + 2

note: (-1)^n = 1 if n is an even number, and (-1)^n = -1 if n is an odd number

since n = 63 (an odd number), (-1)^63 = -1 [you can check this on a calculator]

g(-1) = -1 + 3 + 2

g(-1) = 4


. . . . f(g(-1)) means you should substitute g(-1) for every x in the equation

f(x) = x² + 3x - 1

f(g(-1)) = [g(-1)]² + 3*[g(-1)] - 1

. . . . since g(-1) = 4, you should substitute 4 wherever g(-1) appears in the equation


f(g(-1)) = 4² + 3*(4) - 1

f(g(-1)) = 16 + 12 - 1


f(g(-1)) = 27


>>> the final answer is: f(g(-1)) = 27, choice e)




Thanks for writing.

Staff
www.solving-math-problems.com



Mar 13, 2012
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by: Anonymous

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Thomas

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