Practice Quiz

SAT Math

Category - Algebra and Functions

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If f(x − 3) = (x + 2)/(x − 4), what is the value of f(x)?
  1. (x − 5)/(x − 1)
  2. (x + 5)/(x − 1)
  3. (x − 5)/(x + 1)
  4. (x + 5)/(x + 1)
  5. (x + 1)/(x − 5)
Explanation
Answer: B - The value of f(x) is (x + 5)/(x − 1). Substitute x - 3 with t.
t = x − 3⟹x = t + 3
f(t) = (t + 3 + 2)/(t + 3 − 4) = (t + 5)/(t − 1)
Replace t with x.
f(x) = (x + 5)/(x − 1)
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