3. Suppose that f and g are bijective functions from S into itself sat- isfying go...
O GRAPHS AND FUNCTIONS Composition of a function with itself Suppose that the functions fand g are defined as follows. f(x)--, x#0 g(x)-x2-9 Find the compositions f fand g'g. Simplify. your answers as much as possible. Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the doma Explanation Check
7. We list several pairs of functions f and g. For each pair, please do the following: Determine which of go f and fog is defined, and find the resulting function(s) in case if they are defined. In case both are defined, determine whether or not go f = fog. (a) f = {(1,2), (2,3), (3, 4)} and g = {(2,1),(3,1),(4,1)). (b) f = {(1,4), (2, 2), (3, 3), (4,1)} and g = {(1, 1), (2, 1), (3, 4),(4,4)}. (c)...
4 - Let f(x) = 4 – 5x and g(x) = 2 4 be functions from R into R. Prove that f and g are inverse functions by demonstrating that fog=iR and go f = ir.
Consider the functions f(x) – 2x + 7 and g(x) = (x+3. Determine each of the following. fog(x) = Give the domain of fo g(x). go f(x) = Give the domain of go f(x).
(e) Given the functions x 4y 4 Z show that: (i) if both f and g are injective then the composite gof is also injective. (ii) if both f and g are surjective then the composite gof is also surjective. ii) if both f and g are bijective then the composite gof is also bijective. (e) Given the functions x 4y 4 Z show that: (i) if both f and g are injective then the composite gof is also injective....
Two functions g and f are defined in the figure below. & 3 5 Domain of g Range of g Domain of s Range of Find the domain and range of the composition fºg. Write your answers in set notation. Domain of fog : Range of fog : DO... X $ ? Continue here to search o te a
Composition of two functions: Domai... Two functions g and f are defined in the figure below. 8 0 2 4 3 9 -9 Domain of 8 Range of g Find the domain and range of the composition fog. Write your answers in set notation. Domain of s Range of s Domain of fog : 0 Range of f •8: X ? Explanation Check 2020 M
6. Suppose that f and g are differentiable functions on an interval (a, b), and suppose that for all (a, b) we have f'(z) = g(z) and g'(z) = -f(x). Show that f2+g2 is constant.
Find fog(x), gof(x), and g-1 (x) where f(x) = 2x2 and g(x) = x+3 are functions from R to R.
Suppose that the function F & G are defined as follows Suppose that the functions f and g are defined as follows. f(x) = 5-2x? g(x) = 2 - 6x (a) Find ( 2 )(-1). (a) Find (b) Find all values that are NOT in the domain of If there is more than one value, separate them with commas. (b) Value(s) that are NOT in the domain of