Let f(x) = (3/2)x2, −1 < x < 1. (a) Find P(X > 1/2). (b) Find P(X2 > 1/2). (c) Find P(|X − 1/2| < 1/4). (d) Find the CDF F(x).

Q: let f(x)= X be 1 213 (-√5 < X<√) Y.V Pind P{/X/7/1.5},

A:

Q: (b) Find f-¹(y) for f(x) = √²-1.

A:

Q: Let f(x) = { 3x² + 2, بی کر 2x - 3, if x < 3 if x ≥ 3 be a piecewise function. Evaluate 3 √₁³ f(x)…

A: It is known that: ∫xndx=xn+1n+1+C, where C is the integration constant.

Q: Find the intervals on which f (x) = x2 − 2x − 3 is monotonic.

A: we have to find the interval on which f(x) = x2 − 2x − 3 is monotonic.

Q: Find the domain of (f • g) where f (x) and g (x) = Vx + 4.

A:

Q: Let 7 (t) = Find 7 (t) デ'(t) =D<

A: r'(t) =d(r(t))/dt

Q: Find h(0), h(x + 3), and h(-x) for h(x) = x + Vx² – 1. 2)

A:

Q: f(x) — 3(8х- х?)/256 for 0<x. Determine P(2<X<4)

A: It is given that,

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: f(x) = x* + x³ – 2x² For the above function state all intervals of x where f(x) is positive.

A: solve the following

Q: Let f(x) = -4x+ 2. Find the largest & so that f(x) - f(a)| < e when |x-a| < 8. S .

A:

Q: Suppose f(x) = a and g(x) z2-100 Find a) f[g(x)] and b) domain of f[g(x)]

A:

Q: (27) Let X = P(2) and )E(5-5x) finc

A: Given X≈Pλ That is, EX=λ

Q: QLa f R R be given by f(x)=+3 Find (a){x: (x)=28} (8)The pre-image of 39 and 2 under f.

A: The given function is- fx=x2+3 Putting fx=28, 28=x2+3x2=25x=-5,5

Q: 1. Let f(r) and g(a) 4x + 1. 4 Then (f o g)(6) (ƒ o g)(x)

A: We have to find function

Q: 8) The arerage f(x) is of the function 5x4 √√5 +1 what 2 on the interval [-1,1]

A:

Q: 2 Let f(x)= 3x - 4 and let g(x) = 2x + 1. Find the given value. fig(3)] f[g(3)] = (Type an integer…

A:

Q: Write f (t) = 5(7)t in the form f (t) = P0ekt for some P0 and k.

A:

Q: Let ( 3x² + 2, f(x) = { 2x - 3, be a piecewise function. Evaluate 5 Sof(x)dx= 3 if x < 3 if x ≥ 3

A: The given function:fx=3x2+2if x&lt;32x-3if x≥3.We need to find ∫35fxdx.

Q: Suppose k>0. What is the domain of F(x) =/k² – x² ?

A: