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Given f(x)=2x2−3 and g(x)=x+4 . What is (fg)(x) ?

A)2x3−12
B)2x2+x+1
C) 2x3+8x2−3x−12
D) −2x2+x+7

User Whymess
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2 Answers

1 vote


(fg)(x)=f(x)g(x)=(2x^2−3)(x+4)=2x^3+8x^2-3x-12

or

(fg)(x)=f(x)g(x)=(2x^2−3)(x+4)=2x^3+8x^2-3x-12

User Guillaume Renoult
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7.6k points
2 votes

Answer :

Option (c) is correct


(fg)(x)=2x^3+8x^2-3x-12

Step-by-step explanation:

Given : functions
f(x)=2x^2-3 and
g(x)=x+4

We have to calculate (fg)(x) and choose the correct from the given options.

Consider (fg)(x) = (f • g)(x) = f(x) • g(x)

That is we have to multiply the two functions.

Consider the given functions
f(x)=2x^2-3 and
g(x)=x+4

Then,


f(x)\cdot g(x) =(2x^2-3)(x+4)

Multiply the each term of first bracket with each term of second bracket, we have,


f(x)\cdot g(x) =2x^2\cdot (x+4)-3\cdot(x+4)

Simplify, we have,


f(x)\cdot g(x) =2x^3+8x^2-3x-12

Thus,
(fg)(x)=2x^3+8x^2-3x-12

Option (c) is correct.

User Abhishek Keshri
by
8.5k points