SOLUTION: 1. Let f(x)= (x^2)-5 and g(x)= (3x)^2. Find g(f(x)). ANSWER CHOICES A. (3x^4)-(30x^2)+75 B. (3x^4)-15 C. (3x^4)-5 D. (9x^4)-5 2. Let f(x)= (x^2)-4 and g(x)= (-3x)^2. Find

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Question 595884: 1. Let f(x)= (x^2)-5 and g(x)= (3x)^2. Find g(f(x)).
ANSWER CHOICES
A. (3x^4)-(30x^2)+75
B. (3x^4)-15
C. (3x^4)-5
D. (9x^4)-5
2. Let f(x)= (x^2)-4 and g(x)= (-3x)^2. Find f(g(x)).
ANSWER CHOICES
A.(-3x^4)+12
B.(-3x^4)+ (24x^2)-48
C.(9x^4)-4
D.(-3x^4)-4
NOTE: Please help me with both questions.

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
# 1

Simply start with g(x) = 3x^2 and replace 'x' with f(x). Then replace f(x)
on the right side with x^2-5 and simplify.

g(x) = 3x^2

g(f(x)) = 3(f(x))^2

g(f(x)) = 3(x^2-5)^2

g(f(x)) = 3(x^4 - 10x^2 + 25)

g(f(x)) = 3x^4 - 30x^2 + 75

So the answer is choice A
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# 2

Same idea as in #1, but now in reverse.

f(x) = x^2 - 4

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

f(g(x)) = (-3x^2)^2 - 4

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

So the answer is choice C