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Is the square root of 4 just 2 or both 2 and -2?

f(g(x)) = sqrt(x^2+4x+4), so would I use the domain of g(x) as the domain of f(g(x))?

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f(x) = sqrt(x+1), and has a restricted domain of [0, infinity) g(x) = x^2+4x+3, and has a restricted domain of (-infinity, -3] How would i find the range of f(g(x)) without a calculator?

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Thanks Also, how do you tell if something is conditional? The length of music pieces (in minutes) played daily on Classical FM from 12 noon is a continuous random variable X with pdf given by f(x) = 0.025e^(-0.025x), x>=0 0, elsewhere a. Find the probability, correct to 4 decimal places...

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A new TV lottery game consists of the random selection, with replacement, of 3 marbles from a barrel. The 3 marbles are drawn from a group of 8 identical marbles except for colour. 3 of the marbles are blue and 5 are yellow. If X represents the number of blue marbles in the sample of 3, complete...

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n a tidal river, the time between high tides and low tides is 12 hours. The average depth of water at a point in the river is 5m. At high tide the depth is 8 m. Assume that the depth of the water, h(t) m, at this point is given by h(t) = A sin(nt+e)+b, where t is the number of hours after noon...

A metal worker is required to cut a circular cylinder from a solid sphere of radius 5 cm. Express r in terms of h, where r cm is the radius of the cylinder and h cm is the height of the cylinder. Hence show that the volume, V cm^3, of the cylinder is given by V = (1/4)(pi)(h)(100-h^2)

A rectangle is defined by vertices N and P(x,y) on the curve with equation y = 16-x^2 and vertices M and Q on the x axis a.i. Find the area, A of the rectangle in terms of x ii. state the implied domain for the function defined by the rule given in part i Can someone please help me with this?

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An open tank is to be made from a sheet of metal 84 cm by 40 cm by cutting congruent squares of side length x cm from each of the corners. I've found the volume to be = (84-2x)(40-2x)(x) State the maximal domain for V when it is considered as a function of x. Confused how to do this part Any...

let f: [0, pi/2] → R, where f(x) = cos(3x) -2. The graph of f is transformed by a reflection in the x-axis followed by a dilation of factor 3 from the y-axis. How would you work out the resulting graph, super confusing so wold greatly appreciate if someone helped out:)

The equation of the image of the graph of y = sin x under a transformation of a dilation of factor 1/2 from the y-axis followed by a translation of pi/4 units in the positive direction of the x axis is: I'm narrowed it down two 2 options, but don't know which one is correct. Can someone please...

Bump Can somebody PLEASE ANSWER all my questions above?