Express the function f : X → R given by f(x) = x3 + 1 as set of orde

1.	Express the function f : X → R given by f(x) = x3 + 1 as set of ordered pairs, where X = {–1, 0, 3, 9, 7}.
Answer» Given, X = {–1, 0, 3, 9, 7} f : X → R and f(x) = x³ + 1 When x = –1, we have f(–1) = (–1)³ + 1 ⇒ f(–1) = –1 + 1 ∴ f(–1) = 0 When x = 0, we have f(0) = 0³ + 1 ⇒ f(0) = 0 + 1 ∴ f(0) = 1 When x = 3, we have f(3) = 3³ + 1 ⇒ f(3) = 27 + 1 ∴ f(3) = 28 When x = 9, we have f(9) = 9³ + 1 ⇒ f(9) = 729 + 1 ∴ f(9) = 730 When x = 7, we have f(7) = 7³ + 1 ⇒ f(7) = 343 + 1 ∴ f(7) = 344 Thus, f = {(–1, 0), (0, 1), (3, 28), (9, 730), (7, 344)}

Express the function f : X → R given by f(x) = x3 + 1 as set of ordered pairs, where X = {–1, 0, 3, 9, 7}.

Answer»

Given,

X = {–1, 0, 3, 9, 7}

f : X → R and

f(x) = x³ + 1

When x = –1, we have

f(–1) = (–1)³ + 1

⇒ f(–1) = –1 + 1

∴ f(–1) = 0

When x = 0, we have

f(0) = 0³ + 1

⇒ f(0) = 0 + 1

∴ f(0) = 1

When x = 3, we have

f(3) = 3³ + 1

⇒ f(3) = 27 + 1

∴ f(3) = 28

When x = 9, we have

f(9) = 9³ + 1

⇒ f(9) = 729 + 1

∴ f(9) = 730

When x = 7, we have

f(7) = 7³ + 1

⇒ f(7) = 343 + 1

∴ f(7) = 344

Thus,

f = {(–1, 0), (0, 1), (3, 28), (9, 730), (7, 344)}