If g(x) = x² + x - 1 and (g∘f)(x) = 4x² – 10x + 5, then f(3/4) is equal to
If g(x) = x² + x - 1 and (g∘f)(x) = 4x² – 10x + 5, then f(3/4) is equal to
Option 1 -
3/2
Option 2 -
1/2
Option 3 -
-3/2
Option 4 -
-1/2
Asked by Shiksha User
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1 Answer
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Correct Option - 4
Detailed Solution:g (f (x) = f² (x) + f (x) - 1.
g (f (5/4) = f² (5/4) + f (5/4) - 1.
Given g (f (5/4) = 5/4, let f (5/4) = y.
-5/4 = y² + y - 1 (There appears to be a typo in the image's solution)
y² + y - 1 + 5/4 = 0
y² + y + 1/4 = 0
(y + 1/2)² = 0
y = -1/2.
So, f (5/4) = -1/2.
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