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 are defined by f(x) = 2x + 3 and g (x) = x2 + 7, Then the value of x such that g (f(x)) = 8 are
  • a)
    1, 2
  • b)
    -1, 2
  • c)
    -1, -2
  • d)
    1, -2
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
are defined by f(x) = 2x + 3 and g (x) = x2 + 7, Then the value of x s...
Given that f(x) = 2x + 3, g(x) = x2+7
∴   g(f(x)) = g(2x + 3) = (2x + 3)2 + 7
= 4x2 + 9 + 12x+ 7 = 4x2 + 12x + 16
Given that g (f (x)) = 8
⇒ 4x2 + 12x + 16 = 8
⇒ 4x2 + 12x + 8 = 0
⇒ 4(x2 + 3x + 2) = 0
⇒ 4(x + l)(x + 2) = 0
∴ x = -1 and x = -2
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Most Upvoted Answer
are defined by f(x) = 2x + 3 and g (x) = x2 + 7, Then the value of x s...
G(f(x))=8
(2x+3)^2+7=8
4x^2+9+12x+7=8
4x^2+12x+16-8=0
x^2+3x+2=0
x(x+2)+1(x+2)=0
(x+1)(x+2)=0
x=-1,-2
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Community Answer
are defined by f(x) = 2x + 3 and g (x) = x2 + 7, Then the value of x s...
G(f(x)) = (2x+3)^2+7=8
= 4x^2+12x+8
= x^2+3x+2
= (x+1)(x+2)
= x=-1,-2
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