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Elementary Functions

19 practice questions with full worked solutions. Free, no account needed.

Problems & worked solutions

Problem #0241 International

Problem 1 — Elementary Functions

For f:R→R, f(x)=x3, the value of f(−2) is:

Show answer & worked solution
  1. A. −8✓ correct
  2. B. −6
  3. C. 6
  4. D. 8

f(−2)=(−2)3=−8.

Problem #0242 International

Problem 2 — Elementary Functions

The maximal domain of f(x)=x−4 is:

Show answer & worked solution
  1. A. R
  2. B. (−∞,4]
  3. C. [4,+∞)✓ correct
  4. D. (4,+∞)

x−4≥0⇔x≥4. The domain is [4,+∞).

Problem #0243 International

Problem 3 — Elementary Functions

The solution of x+2=3 is:

Show answer & worked solution
  1. A. 1
  2. B. 5
  3. C. 7✓ correct
  4. D. 11

x+2=9⇒x=7. Check: 9=3 ✓.

Problem #0920 US SAT

Problem 4 — Exponential Function

For f(x)=2x, the value of f(3) is:

Show answer & worked solution
  1. A. 6
  2. B. 9
  3. C. 8✓ correct
  4. D. 5

f(3)=23=8.

Problem #0921 US SAT

Problem 5 — Logarithmic Function

The value of log⁡28 is:

Show answer & worked solution
  1. A. 4
  2. B. 2
  3. C. 3✓ correct
  4. D. 1

23=8, so log⁡28=3.

Problem #0919 US SAT

Problem 6 — Power Function

For f(x)=x3, the value of f(−2) is:

Show answer & worked solution
  1. A. −8✓ correct
  2. B. 8
  3. C. −6
  4. D. 6

f(−2)=(−2)3=−8.

Problem #0922 US SAT

Problem 7 — Radical Function

The domain of f(x)=x−4 is:

Show answer & worked solution
  1. A. R
  2. B. [4,∞)✓ correct
  3. C. (4,∞)
  4. D. (−∞,4]

Require x−4≥0, i.e. x≥4.

Domain: [4,∞).

Problem #0765 FR Spé

Problem 8 — Exponential Function

Solve over R the equation e2x−4ex+3=0. The solution set is:

Show answer & worked solution
  1. A. {0 ; ln⁡3}✓ correct
  2. B. {1 ; 3}
  3. C. {ln⁡3}
  4. D. {1 ; ln⁡3}

Set X=ex, so X > 0. The equation becomes X2−4X+3=0 (X−1)(X−3)=0 X=1orX=3 Both roots are positive, so substitute back: ex=1  ⟹  x=0 ex=3  ⟹  x=ln⁡3 The solution set is {0 ; ln⁡3}.

Problem #0247 International

Problem 9 — Elementary Functions

For x∈(0,1), which inequality is correct?

Show answer & worked solution
  1. A. x2<x3
  2. B. x3<x2✓ correct
  3. C. x2=x3
  4. D. It depends on the specific value of x

For x∈(0,1), multiplying by x shrinks the value: x3=x⋅x2<x2 since 0<x<1.

Problem #0248 International

Problem 10 — Elementary Functions

The value of f(x)=x−2 at x=3 is:

Show answer & worked solution
  1. A. −9
  2. B. 19✓ correct
  3. C. −6
  4. D. 9

f(3)=3−2=132=19.

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