Step-by-step explanation:
1.f(x)=2x²-1
a. f(2t)
f(2t)=2(2t)²-1
= 8t²-1
b. f(x+1)
f(x+1)= 2(x+1)²-1
= 2(x²+2x+1)-1
=2x²+4x +2 -1
= 2x²+4x+1
2.a. g(x-1)
3x -3x²
3(x-1) -3(x-1)²
3x-3 -3(x²-2x+1)
3x -3 -3x²+6x-3
-3x²+9x-6
x²-3x+2
(x-1)(x-2)
b. 3(-3k) -3(-3k)²
-9k -3(9k²)
-9k -27k²
-27k² -9k
-9k(3k+k)
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Answers & Comments
Step-by-step explanation:
1.f(x)=2x²-1
a. f(2t)
f(2t)=2(2t)²-1
= 8t²-1
b. f(x+1)
f(x+1)= 2(x+1)²-1
= 2(x²+2x+1)-1
=2x²+4x +2 -1
= 2x²+4x+1
2.a. g(x-1)
3x -3x²
3(x-1) -3(x-1)²
3x-3 -3(x²-2x+1)
3x -3 -3x²+6x-3
-3x²+9x-6
x²-3x+2
(x-1)(x-2)
b. 3(-3k) -3(-3k)²
-9k -3(9k²)
-9k -27k²
-27k² -9k
-9k(3k+k)