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Question
Let f: R → R be defined by f(x) = 3x 2 – 5 and g: R → R by g(x) = `x/(x^2 + 1)` Then gof is ______.
Options
`(3x^2 - 5)/(9x^4 - 30x^2 + 26)`
`(3x^2 - 5)/(9x^4 - 6x^2 + 26)`
`(3x^2)/(x^4 + 2x^2 - 4)`
`(3x^2)/(9x^4 + 30x^2 - 2`
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Solution
Let f: R → R be defined by f(x) = 3x 2 – 5 and g: R → R by g(x) = `x/(x^2 + 1)` Then gof is `(3x^2 - 5)/(9x^4 - 30x^2 + 26)`.
Explanation:
Given that, f(x) = 3x2 – 5 and g(x) = `x/(x^2 + 1)`
gof(x) = g(f(x))
= g(3x2 – 5)
= `(3x^2 - 5)/((3x^2 - 5)^2 + 1)`
= `(3x^2 - 5)/(9x^4 - 30x^2 + 25 + 1)`
= `(3x^2 - 5)/(9x^4 - 30x^2 + 26)`
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