AP EAMCET Algebra: Functions — practice questions
74 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice AP EAMCET Algebra: Functions in the app →In a function from set X to set Y, what is the set X called?The set of all actual output values of a function is called itsWho first used the functional notation f(x), in the year 1734?In the arrow notation x ↦ x + 1, the symbol ↦ is read asMultiplication of integers is a function of how many variables?Count the functions that send the set {p, q, r} into the set {0, 1}.A has 2 elements and B has 4. How many functions map A into B?If f(x) = 3x + 2, what is the value of f(4)?To make f(x) = x² one-to-one, its domain can be restricted toA function f is one-to-one if f(x1) = f(x2) always impliesAnother name for an injective function is aThe horizontal line test is used to check whether a function isHow many one-to-one functions exist from a 3-element set to a 5-element set?A function has an inverse function exactly when it isFind the inverse of the linear rule f(x) = 5x - 7.If y = (2x + 8)³, then x expressed in terms of y isHow many inverse functions can an invertible function have?The notation f⁻¹ for an inverse function was introduced byWhich expression denotes the reciprocal of f(x), not its inverse function?A function that is equal to its own inverse is called a(n)Which function satisfies f(f(x)) = x for every nonzero real x?For invertible f and g, the inverse of g∘f equalsFor f(x) = 3x and g(x) = x + 5, find f(g(x)).With f(x) = 2x + 4 and g(x) = x³, the value of f(g(2)) isf maps 1,2,3,4 to 1,3,1,2 and g maps 1,2,3,4 to 2,3,1,2. Find g(f(2)).Which property does composition of functions always satisfy?For general functions f and g, f(g(x)) and g(f(x)) areg(f(x)) is meaningful only if the codomain of f lies inside theIf f and g are both one-to-one, then g∘f isRepeated composition of a function with itself is calledA function f(x) = x² is composed with itself three times. What is f(f(f(x)))?All bijections of a set onto itself form a group called theCayley's theorem says every group is a subgroup of aDerivatives of composite differentiable functions are found using theIn trigonometry, tan⁻¹ x usually denotesOn which interval is sin x one-to-one?The curve of an inverse function is the original curve reflected acrossA continuous function on an interval is invertible on its range if it isIf f: X → Y is invertible, then f⁻¹ has domainThe inverse of the inverse function f⁻¹ isThe positive square root is the inverse of x² restricted toA partial function from X to Y is called total when its domain of definition equalsA function can be represented by the set of all ordered pairs of the formA function is a binary relation in which each x in X is related toWhich relation from {1,2,3} to {a,b} is NOT a function?A bijective function is one that is bothThe identity function on a set X sends each element x toA function from a set X into the one-element set {s} sends every x toIn the composite g∘f, which function is applied first?If f sends every integer to 0, the preimage of 0 isThe real function f(x) = x/(x² - 4) is undefined atIf g(f(x)) = 6x + 5 where f(x) = 2x + 1, then g(x) equalsIf F = 9C/5 + 32 converts Celsius to Fahrenheit, the inverse formula is C =A differentiable function with always positive derivative on an interval isThe set of images of all elements of the domain is called theA surjective function is also called a function that isWhat is the inverse of the function f(x) = 2x + 3?A function defined on a domain with a single element is alwaysThe inclusion of a set X into itself is called theA function equal to its own inverse, so that f composed with f is the identity, is called anWhen an inverse function of f exists, how many inverses can f have?If f(x) = 2x + 1, what is f(f(1)), the second iterate of f at 1?If f is a restriction of g, then g is called an ____ of f.Restricting the domain of f(x) = x^2 to the nonnegative reals makes itWhich real number must be excluded from the domain of f(x) = 1/(x - 5)?A quotient of two polynomial functions is called aA function whose domain is the set of natural numbers is called aHow many injective functions map a 2-element set into a 3-element set?In a function from X to Y, the set Y that receives the outputs is called what?A function assigns to each element of its domain how many elements of the codomain?If f(a) differs from f(b) whenever a and b are different inputs, f is called what?A function whose range equals its whole codomain is known by which name?A function that is both one-to-one and onto is described as what?A function is injective exactly when each output value has a preimage with how many elements?