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Find the following values for the given functions. f ( x ) = x + 8, g ( x ) = x^2 (a) ( f + g )(8) 80 80 (b) ( f โ g )(8) -48 - (c) ( fg )(8) 1024 1024 (d) ( f / g )(8) .25 1/ 2.6.66/6.66 points Consider the following functions. f ( x ) = x + 3 6 , g ( x ) = x + 3 6 (a) Find ( f + g )( x ), ( f โ g )( x ), ( fg )( x ), ( f / g )( x ). ( f + g )( x ) = ( f โ g )( x ) = ( fg )( x ) = ( f / g )( x ) = (b) Find the domain of f + g. (Enter your answer using interval notation.) Find the domain of f โ g. (Enter your answer using interval notation.) Find the domain of fg. (Enter your answer using interval notation.) (c) Find the domain of f / g. (Enter your answer using interval notation.) Practice Another Version Practice Another Version
Consider the following functions. f ( x ) = |8 x |, g ( x ) = โ (a) Find ( f โ g )( x ). = (b) Find ( g โ f )( x ). = (c) Find f ( g (โ2)). 32 32 (d) Find g ( f (3)). -4 - 4.5/6.66 points Consider the functions below. f ( x ) = 6 x - 7, g ( x ) = 4 x^2 - x + 7 (a) Find ( f โ g )( x ) ( f โ g )( x ) = (b) Find ( g โ f )( x ) ( g โ f )( x ) = (c) Find ( f ( g (-2)) f ( g (-2)) = (d) Find ( g ( f (3)) g ( f (3)) = 5.6.66/6.66 points | Previous AnswersMy Notes Let f ( x ) = 14 x^2 and g ( x ) = 1 1+ 2 x Determine the value of gโf (x). gโf (x) = Practice Another Version Practice Another Version Practice Another Version
8.6.66/6.66 points The functions f, g, and h are defined below: f ( x ) = 4 x + 9 g ( x ) = x^2 + 5 x + 6 h ( x ) = 1 โ 6 x^2 Classify each of the following compositions of functions as linear , quadratic , or neither. f(g(x)) linear quadratic neither f(f(x)) linear quadratic neither h(g(x)) linear quadratic neither 9.6.66/6.66 points | Previous AnswersMy Notes Solve the equation ( f โ g )( x ) = 0 using the given functions. f ( x ) = x^2 โ 6 g ( x ) = x + 3 x = (smaller value) x = (larger value) 10.6.66/6.66 points Practice Another Version Practice Another Version Practice Another Version
Several values of two functions T and S are listed in the tables. t 5 8 6 0 4 T ( t ) 6 0 8 5 1 x 5 8 6 0 4 S ( x ) 8 5 0 6 1 Find the expressions, if possible. (If it is not possible, enter NONE.) (a) ( S โ T )(8) ( S โ T )(8) = 6 6 (b) ( T โ T )(8) ( T โ T )(8) = 5 5 (c) ( S โ S )(8) ( S โ S )(8) = 8 8 (d) ( T โ S )(4) ( T โ S )(4) = NONE NONE 11.6.66/6.66 points | Previous AnswersMy Notes Consider the following functions. f ( x ) = x^3 + 8, g ( x ) = (^3) x โ 8 (a) Find ( f โ g )( x ).= Find the domain of f โ g. (Enter your answer using interval notation.) (b) Find ( g โ f )( x ).= Find the domain of g โ f. (Enter your answer using interval notation.) Practice Another Version Practice Another Version
It has been estimated that 1000 curies of a radioactive substance introduced at a point on the surface of the open sea would spread over an area of 70,000 km^2 in 70 days. This means that the function g(t) = 1000t represents the contaminated area as a function of time, the number of days since contamination. From geometry, you can create a function r = f(A) that expresses the radius of a circle as a function of area. (a) Express the radius as a function of A (upper case!). f(A) =
Find the symbol ฯ in the CalcPad or type pi.
(b) what does the composite function f โ g (t) model? The radius of the contamination as a function of time The area of the contamination as a function of time The area of the contamination as a function of radius The radius of the contamination as a function of area 14.6.66/6.66 points In astronomy, distances to stars are measured in light years. One light year is the distance a ray of light travels in one year. If the speed of light is approximately 186,000 miles per second, estimate the number of miles in five light years. (Round your answer to three significant figures.)
2.935 2.93 ร 10 13 13 mi
15.6.76/6.76 points The population dynamics of many fish are characterized by extremely high fertility rates among adults and very low survival rates among the young. A mature specimen of a particular fish may lay as many as 3.5 million eggs, but only 0.00015% of the offspring survive to the age of 3 years. Use scientific form to approximate the number of offspring that live to age 3. (Round your answer to the nearest whole number.) 5 5 offspring Practice Another Version Practice Another Version
