Consider the following functions: f(x) = 7x+3 g(x) = √/7 (3-x) r(x) = Evaluate/Simplify th follow 7x x-3

The volume V in cubic inches of a sphere with radius r in inches is given by the function V(r) = (4/3)??^3a) Find V(6) and explain its meaning.b) Find V−1 (?) and explain its meaning.

Let f(x) = √√x+3 and g(x) = 6x − 2. Find each of the following composite functions and state the domain: (a) fog (b) gof, (c) fof (d) gog

A scientist observed that the speed S at which certain ants ran was a function of T, the ambient temperature.† He discovered this could be determined by the formula below where S is measured in centimeters per second and T is in degrees Celsius. S = 0.2T − 2.7 (a) Using functional notation, express the speed of the ants when the ambient temperature is 14 degrees Celsius.S (  )Calculate that speed using the formula above. (Round your answers to one decimal place.) cm/sec(b) Solve for T in the formula above to obtain a formula expressing the ambient temperature T as a function of the speed S at which the ants run.T =        (c) If the ants are running at a speed of 3 centimeters per second, what is the ambient temperature? (Round your answer to one decimal place.) °C

Determine the value of x so that x-2 =1/9

Use the given functions to calculate each operation and simplify.   f(x)=1/x-9    g(x)=-7x-4   h(x)=-x2+9   j(x)= |x|   a. (h+j)(-4)= b. (g-j)(-8)= c. (gh)(5)= d. (j/f)(2)=   I'm having trouble with this problem.

Find f. = 6 + 6x + 36x², f(0) = 3, f(1) f(1) = 14 f"(x) =

Let f(æ) = 2x + 3 and g(æ) = 2a2? + 4x. After simplifying, (f o g)(x) =

find x when f(x)=295

Consider the function f(x)=x2+6(5x−10)(x+4)f(x)=x2+6(5x-10)(x+4). For each prompt below, if no solution exists - enter "DNE". If there is more than one solution, enter your answer as a comma-separated list (like "1, 3"). You may find it helpful to rewrite the numerator or denominator in a different form to help you complete some of the parts. Determine the vertical intercept of ff. f(0)=f(0)=    Determine the zeros (or "roots") of ff. x=x=    Determine the vertical asymptote(s) of ff. x=x=    Determine the horizontal asymptote of ff. y=y=