Advertisements
Advertisements
प्रश्न
If f, g : R → R are defined by f(x) = |x| + x and g(x) = |x| – x find g o f and f o g
Advertisements
उत्तर
f(x) = |x| + x = `{{:(x + x = 2x, "if" x ≥ 0),(- x + x = 0, "if" x < 0):}`
g(x) = |x| – x = `{{:(x - x = 0, "if" x ≥ 0),(- x - x = - 2x, "if" x < 0):}`
f o g(x) = f(g(x)) = `{{:(f(0), "if" x ≥ 0),(f(- 2x), "if" x < 0):}`
f o g(x) = `{{:(2 xx 0 = 0, "if" x ≥ 0),(- x + 2x = 0, "if" x < 0):}`
∴ f o g(x) = 0 for all x ∈ R
g o f(x) = g(f(x)) = `{{:(g(2x), "if" x ≥ 0),(g(0), "if" x < 0):}`
g o f(x) = `{{:(0, "if" x ≥ 0),(0, "if" x < 0):}`
⇒ g of(x) = 0 for all x ∈ R
APPEARS IN
संबंधित प्रश्न
Suppose that 120 students are studying in 4 sections of eleventh standard in a school. Let A denote the set of students and B denote the set of the sections. Define a relation from A to B as “x related to y if the student x belongs to the section y”. Is this relation a function? What can you say about the inverse relation? Explain your answer
Write the values of f at − 4, 1, −2, 7, 0 if
f(x) = `{{:(- x + 4, "if" - ∞ < x ≤ - 3),(x + 4, "if" - 3 < x < -2),(x^2 - x, "if" - 2 ≤ x < 1),(x - x^2, "if" 1 ≤ x < 7),(0, "otherwise"):}`
State whether the following relations are functions or not. If it is a function check for one-to-oneness and ontoness. If it is not a function, state why?
If A = {a, b, c} and f = {(a, c), (b, c), (c, b)}; (f : A → A)
State whether the following relations are functions or not. If it is a function check for one-to-oneness and ontoness. If it is not a function, state why?
If X = {x, y, z} and f = {(x, y), (x, z), (z, x)}; (f : X → X)
Let A = {1, 2, 3, 4} and B = {a, b, c, d}. Give a function from A → B of the following:
neither one-to-one nor onto
Let A = {1, 2, 3, 4} and B = {a, b, c, d}. Give a function from A → B of the following:
not one-to-one but onto
Let A = {1, 2, 3, 4} and B = {a, b, c, d}. Give a function from A → B of the following:
one-to-one but not onto
Find the largest possible domain of the real valued function f(x) = `sqrt(4 - x^2)/sqrt(x^2 - 9)`
Show that the relation xy = −2 is a function for a suitable domain. Find the domain and the range of the function
If f : R → R is defined by f(x) = 3x − 5, prove that f is a bijection and find its inverse
The weight of the muscles of a man is a function of his body weight x and can be expressed as W(x) = 0.35x. Determine the domain of this function
Choose the correct alternative:
If f(x) = |x − 2| + |x + 2|, x ∈ R, then
Choose the correct alternative:
If the function f : [−3, 3] → S defined by f(x) = x2 is onto, then S is
Choose the correct alternative:
Let X = {1, 2, 3, 4}, Y = {a, b, c, d} and f = {(1, a), (4, b), (2, c), (3, d), (2, d)}. Then f is
Choose the correct alternative:
The inverse of f(x) = `{{:(x, "if" x < 1),(x^2, "if" 1 ≤ x ≤ 4),(8sqrt(x), "if" x > 4):}` is
