Consider the cases: (1) x = -4 (2) x = –2 (3) x = 0 (4) x = 2 (5) x = 4 Part (a) For each case, state whether or not f is continuous at the given point: (Enter "y" for yes, "n" for no.) (1) (2) (3) (4) (5) Part (b) For each case, determine if f is continuous from the right, or from the left, or neither. (Enter "r", "l", or "n", respectively below. In the case of continuity at a point from both sides, enter "b".) (1) (2) (3)

Q: Let f be a function of x. Then f (10x) = 10 (f (x)). O True O False

A: the answer for the above statement is false. the explanation is given in the below step

Q: Evaluate  f(−7), f(0), and f(3)  for the piecewise defined function. f(x) =    x + 2     if x < 0…

A:

Q: Given f(x) = 23 10x, evaluate the following. (a) (f of-)(42) = (b) (f o f)(40) = %3D

A: First we will calculate the inverse of f. Then see that the composition of f and f inverse works…

Q: f(x) = -7x + 6 x² +6 if x < 0 if x 20

A:

Q: Let g(x)=31-x. Compute: a) g(2.3) b) g(2) c) g(-1)

A: Given that

Q: if f(x) = 3 and g(x) = f(x) – 1 then (f .g)(-3) О а.-3 O b. 6 C. 9 Od. 27

A:

Q: 4. Determine each value for the given function: f (5) = %3D 3", if x 0

A:

Q: Let f (x)=x* +2x – 3.x? – 4x +4. Find: (a) the intervals on which f (x) is increasing or decreasing.

A: Given that:  f(x) = x4 + 2x3 - 3x2 -4x + 4   find intervals on which f(x) is increasing or…

Q: If 10x³y* + e*Y = 5 defines y implicitly as a function of x, find y.

A: Using derivatives of implicit function.

Q: Determine whether the following function is continuous at the given point z- 3z+ 14z -5 f(2) 3z -1…

A: A function fx is continuous at x=a if limx→a-f(x) = limx→a+f(x) = f(a)  Given: fx=3x2+14x-53x-1…

Q: 5.) Evaluate f(-3) for f(x) = x³ +3x + 17

A: Given  f(x) =x3+3x+17

Q: If f(x) = 2x2+x +1, and g(x)=x is an identity function then (f + g)(1) = O a. - 4 O b. -8 O C. 4 O…

A:

Q: If f(x) = x*3 − 6/x, find the following:a) f(-1/2)b) f(2)c) f(-2)

A: Answer: a) -27/2 or -13.5

Q: Consider the following functions. f={(−2,1),(2,−4),(4,−4),(−1,1)}f={(−2,1),(2,−4),(4,−4),(−1,1)}…

A:

Q: What is the physical meaning of |xd(f)| and <Xd(f)?

A: The physical meaning of |x d(f)| and &lt;X d(f) will be-  |x d(f)| =   It defines (gives) the value…

Q: Let f(x) = 3 In ((0+1) 2x 2-25)-In(2(0+1) x-10): a. Simplify f(x) b. If f(x) = 4, find x.

A: Use the following properties of the logarithmic function to simplify this equation. ln a-ln b =…

Q: If f(x) = ax, show that f(A + B) = f(A) . f(B).

A: given: fx=ax we have to show that f(A + B) = f(A) . f(B)

Q: 2 V1-x*

A:

Q: 3. Determine the monotonicity of the following function: f(x) = -x3 – 3x + 6

A:

Q: 25. Let f(x) = 5x² + 1. Evaluate and simplify each of the following: f(4)-f(1) 4-1 (A) (Bu PC (B)…

A: Given function is we have to evaluate the following  and simplify them