Exercises for Daily Test 3 for Science Class
A. Function
1. Let 𝑓(𝑥) = 𝑥 2 − 2𝑥 − 48 and 𝑔(𝑥) = 3𝑥 − 4.
a. Find 𝑓(7) + 𝑔 (5).
b. Find 𝑓 (5) + 𝑔(7).
c. If 𝑓(𝑎 + 1) = 9, then find 𝑎 2 .
d. If 𝑔(2𝑏 + 3) = 10, then find 𝑏 2 .
2. Let 𝑓 (𝑥 ) =
𝑎𝑥+𝑏
2𝑥+3
3
, 𝑥 ≠ − 2. If 𝑓(3) = 10 and 𝑓(1) = 2, then find 𝑓(5). (Hint: The first step
is finding 𝒂 𝐚𝐧𝐝 𝒃.)
B. Inverse of Function
3. Let 𝑔(𝑥) =
4𝑥+3
𝑥−3
, 𝑥 ≠ 3.
a. Find 𝑔−1 (1).
b. Find 𝑔−1 (2𝑥 + 1).
4. Let ℎ(𝑥) =
𝑎𝑥+𝑏
3𝑥+2
2
, 𝑥 ≠ − 3. If ℎ−1 (2) = 4 and ℎ −1 (1) = 7, then find ℎ −1 (9).
5. Let 𝑓(𝑥) = 𝑥 2 − 3𝑥 − 1. Find 𝑓 −1 (17).
C. Composite of Functions
6. Let 𝑓(𝑥) =
3𝑥+1
5
, 𝑥 ≠ − 2 and 𝑔(𝑥) = 7𝑥 + 4.
2𝑥+5
a. Determine (𝑓 ∘ 𝑔)(𝑥).
b. Determine (𝑔 ∘ 𝑓)(𝑥).
7. Let 𝑓(𝑔(𝑥)) = 3𝑥 + 10 and 𝑔(𝑥) =
8. Let 𝑓(𝑔 (𝑥 )) =
𝑥+3
7𝑥−3
4
, 𝑥 ≠ 3. Find 𝑓(2).
3𝑥−4
1
, 𝑥 ≠ 2 and 𝑓 (𝑥) = 4𝑥. Find 𝑔(10).
2𝑥−1
Challenge Problems
a. Given 𝑓 (𝑥 ) = √𝑥 2 + 3𝑥 − 4. If √6 ≤ 𝑓 (𝑥) ≤ √66, then find the domain of 𝑓 (𝑥).
1
1
1
3
𝑥
𝑥
2
2
b. Given 3𝑓 (1 + ) + 2𝑓 (1 − ) = 3𝑥 + 1, 𝑥 ≠ 0. Find 𝑓 ( ) and 𝑓 ( ).