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17 Cards in this Set

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 Let f(r) and h(t) be functions with real world meanings. What is the general sentence that describes the meaning of f(h(t))? The real world meaning is: (meaning of f) in terms of (meaning of t). in other words, the meaning of the outermost function with respect to the inner most input. What is the meaning of k(g(t)) where L=k(h) is the length of a steel bar at temperature H and H=g(t) is the temp at time t? meaning of k(g(t)) is the meaning of the outermost function in terms of the inner most input..... Thus k(g(t)) gives the length of a steel bar in terms of the time. If you are given a table of values for f(x), g(x), h(x) and are told to fill in the blanks for h(x)=g(f(x)), then what two functions do you assume have the same input values? h and f What are the steps for finding an inverse function? 1. Take the original equation and solve for the input in terms of the output. 2. Replace the input with f inverse of whatever the question asks 3. Make sure your input for your inverse function matches the variables in the equation True or false: If there is a horizontal line which intersects a functions graph in more than one point, then the function is guaranteed an inverse False. if the line intersects in more than one point, the function does not have an inverse. If you are given a function whose graph fails the horizontal line test, how can you alter the function so that it passes the horizontal line test? Restrict the functions domain so that the horizontal line only intersects the function at one point. The graph of a function and its inverse are symmetric about .... The line y=x. You can also call this being symmetric about the origin If (a,b) is a point on the graph of a function, then what point do we know is on the graph of the inverse function? (b,a) If f(cookies)=milk then what is true of the inverse function? finverse(milk)=cookies Given the domain and range of a function f, what are the domain and range of its inverse? domain=range of f range=domain of f If you are given f and g, how can you algebraically prove that f is the inverse of g and vice versa? show that f(finverse(x))=x or finverse(f(x))=x If g and f are inverses then what is the value of g(f(5/(n^2)-200))? 5/(n^2)-200 True or false, in general, f(g(x))=g(f(x)) false If f(x)=x^2 and g(x)=sin(x), then what is f(g(x))? (sin(x))^2 If f(x)=x^2 and g(x)=(x+3)^0.5 then what is the domain of f(g(x))? Since the numbers under the square root have to be positive, we need x+3>=0 Thus x>=-3 f(x)=x^2 is not restricted at all since this function can make sense of any input. Thus the domain is only restricted by g(x) so the domain is all x>=-3 Do most quadratic functions have inverses? No, quadratic functions have parabolas for their graphs so their graphs will not pass the horizontal line test (unless the domain is restricted) If the formula for the area of a circle is A=(pi)(r)^2, where r=radius and the formula for the circumference is C=(pi)d, where d=diameter, what is the composition of A(C(d)) and what is its meaning? A(C(d))= A((pi)d)=pi((pi)d)^2 A(C(d)) gives the area in terms of the diameter