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If g(x) = 2x^(2) + 3x - 4 and g (f(x)) =...

If `g(x) = 2x^(2) + 3x - 4` and `g (f(x)) = 8x^(2) + 14 x + 1` then f (2) =

A

3

B

5

C

`-3`

D

`-5`

Text Solution

Verified by Experts

The correct Answer is:
B
`g(f(2)) = 8(2)^(2) + 14(2) + 1 =61`
Now , `g(x) = 2x^(2) + 3x - 4`
`g(f(x)) = 2f^(2) (x) + 3f(x) - 4`
`g(f(2)) = 2f^(2) (x) + 3f(x) - 4`
`therefore " " 2f^(2) (2) + 3f(2) - 4 = 61`
solving we get, `f(2) = 5 or -13//2`
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