If fog(x) = x – 3 and f(x) = x^2, what is g(x).
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Tushar Chandra
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We have fog(x) = f(g(x)) = x – 3 and f(x) = x^2 and we need to determine g(x).
Let g(x) = y
=> f(y) = y - 3 = x^2
=> x = sqrt (y – 3)
interchanging x with y gives y = g(x) = sqrt (x – 3)
Check: f(g(x)) = f( sqrt (x – 3)) = [sqrt (x – 3)]^2 = x – 3.
Therefore g(x) = sqrt (x – 3)
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giorgiana1976 | Student
fog(x) = f(g(x))
If f(g(x)) =x - 3 and f(x) = x^2
f(g(x)) = (g(x))^2
But f(g(x)) = x - 3 => (g(x))^2 =x - 3
To determine g(x), we'll apply square root both sides:
sqrt(g(x))^2 = sqrt(x-3)
g(x) = sqrt(x-3)
Student Answers