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✅️Solution 1️⃣7️⃣👆
📌The domain of the function
f(x) = sqrt(4 - x^2)
is the set of all possible values of x that can be plugged into the function that does not cause an error or give undefined output.
📚A square root function is defined only for values of x that make the expression inside the square root non-negative.
That is, (4 - x^2) ≥ 0.
Multiply both sides by negative one, and solve the resulting inequality:
x^2 - 4 ≤ 0
(x-2)(x+2) ≤ 0
Case I
(x-2) ≥ 0 and (x+2) ≤ 0
x ≥ 2 and x ≤ -2 which is empty set.
Case II
(x-2) ≤ 0 and (x+2) ≥ 0
x ≤ 2 and x ≥ -2
-2 ≤ x ≤ 2 which is the closed interval [-2, 2].
Therefore, the domain of the function f(x) = sqrt(4 - x^2) is the interval [-2, 2].
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2️⃣3️⃣Let f(x) = 2x^2 + 3x + 1. What is the equation of the axis of symmetry?
2️⃣2️⃣Let f(x) = x^3 - x^2 + x - 1. What is the equation of the line tangent to the graph of f(x) at the point (1, 0)?
2️⃣1️⃣ Let f(x) = x^2 + 3x - 2 and g(x) = 2x - 1. What is the value of (g ∘ f)(-2)?
2️⃣0️⃣ Let f(x) = e^x and g(x) = ln(x). What is the value of (f ∘ g)(1)?
1️⃣9️⃣Consider the function f(x) = |x - 4|. What is the range of this function?
1️⃣8️⃣If a function f(x) = |x|, what is the value of f(-3)?
1️⃣7️⃣Which of the following is the domain of the function f(x) = sqrt(4 - x^2)?
✅️Solution 1️⃣6️⃣👆👆
The inverse of a function is a new function that "undoes" the original function.
To find the inverse of f(x) = 2x + 3, we can follow these steps:
👉write f(x) with y: y = 2x + 3
👉Swap the positions of x and y:
x = 2y + 3
👉 Solve for y:
x-3 = 2y + 3-3
x-3 = 2y
y = (x - 3)/2
So the inverse of f(x) is
f^-1(x) = (x - 3)/2.
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1️⃣6️⃣Which of the following is the inverse of the function f(x) = 2x + 3?
1️⃣5️⃣Which of the following is the range of the function f(x) = x^2?
1️⃣4️⃣Which of the following is the domain of the function f(x) = 1/x?
1️⃣2️⃣Let A = {a, b, p}, B = {2, 3}, C = {p, q, r, s} then n[(A ∪ C )× B] is:
1️⃣0️⃣ Let A, B, and C be sets. Which of the following represents De Morgan's Law?
9️⃣Let A = {1, 2, 3, 4, 5} and B = {3, 4, 5, 6, 7}. Which of the following represents A ∆ B?
8️⃣Let A = {a, b, c} and B = {b, c, d}. Which of the following represents A - B?
7️⃣Let A = {x | x is a positive integer less than 6} and B = {x | x is an even integer between 4 and 8}. What is A ∩ B?
6️⃣ Let A = {a, b, c} and B = {1, 2, 3}. How many elements are in the Cartesian product A × B?
