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Calculus Functions Practice Questions

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Updated on Oct 1, 2011

To review these concepts, go to Calculus Functions Study Guide.

Calculus Functions Practice Questions

  1. Find the value of f(5) when f(x) = 2x – 1.
  2. Find the value of g( – 3) when g(x) = x3 + x2 + x + 1.
  3. Find the value of h when h(t) = t2+
  4. Find the value of f(7) when f(x) = 2.
  5. Find the value of k( 4) when k(u) = u2 +2 u.
  6. Find the value of h( 64) when h(x) = √x – 3√x.
  7. Suppose that after t seconds, a rock thrown off a bridge has height s(t) = –16t2 + 20t + 100 feet off the ground. How high is it after 3 seconds?
  8. Suppose that the profit on making and selling x cookies is . How much profit is made on 100 cookies?

Simplify the following.

  1. f(y) when f(x) = x2 + 3x – 1
  2. f (y + 1) when f(x) = x2 + 3x – 1
  3. f(x + a) when f(x) = x2 + 3x – 1
  4. g(x2 + √x) when
  5. g(2x) – g(x) when
  6. f(x + a) – f(x) when f(x) = x2 + 4x – 5
  7. when h(x) = 3x + 2
  8. when g(x) = x2 – 2x + 1

Using g(x) = x3 – 2x2 + 1, and h(x) = x – √x, simplify the following compositions.

  1. f g(x)
  2.  g f (x)
  3. f h (t)
  4. f f (x)
  5. h h (x)
  6. g h (9)
  7. h f g (x)
  8.  f h f(2x)

Find the domain of each of the following functions.

  1. 26. h(x) = √x+1
  2.  
  3. g(x) = x2 + 5x – 6
  4.  
  5. h(x) = 3x
  6.  
  7.  

Solutions

  1. f(5) = 9
  2. g( –3) = –20
  3. h = 1
  4. f(7) = 2. Because there is no x in the description of f, the 7 never gets used. This is called a constant function because it is constantly equal to 2.
  5. k(4) = 21
  6. h(64) = 4
  7. The rock is s(3) = 16 feet high after 3 seconds.
  8. The profit on 100 cookies is P(100) = $39.
  9. f(y) = y2 + 3y – 1
  10. f(y + 1) = y2 + 5y + 3
  11. f(x + a) = x2 + 2xa + a2 + 3x + 3a – 1
  12. g(x2 + √x) = – 6(x2 + √x)
  13. g(2x) – g(x) =
  14. f(x + a) – f(x) = (x + a)2 + 4(x + a) – 5 – (x2 + 4x – 5) = 2xa + a2 + 4a
  15.  
  16. = 2x + a – 2
  17.  
  18.  
  19.  
  20.  
  21.  
  22.  g h(9) = g(9 – √9) = g(6) = 145
  23. h f g(x) = h(f(g(x))) =
  24. f h f(2x) =
  25. x ≠ – 3, x ≠ 5
  26. x ≥ –1
  27. t > –5 because t ≠ –5
  28. The domain consists of all real numbers.
  29. a ≠ 0
  30. The domain consists of all real numbers.
  31. x ≤ 2, x ≠ – 8
  32. u > is enough, because it already rules out u ≠ –3 and u.
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