Let R+ be the set of all non- negative real numbers. Show that the fun

1.	Let R+ be the set of all non- negative real numbers. Show that the function f: R+ → [4,∞) given by f(x) = x2 + 4 is invertible and write the inverse of f.
Answer» f(x₁) = f(x₂) X₁² + 4 = X₂² + 4 x₁ = x₂ ∴ f (x) is one-one Let y = f(x) y = 4x + 3 x = y - 3/4 ∈R₊ ∴ f (x) is onto Let f^-1 (x) = y f(y) = x 4y +3 = x y = x - 3/4 ∴ f^-1 : [4,8) → R+ is defined by f^-1 (x) = x - 3/4

Let R+ be the set of all non- negative real numbers. Show that the function f: R+ → [4,∞) given by f(x) = x2 + 4 is invertible and write the inverse of f.

Answer»

f(x₁) = f(x₂)

X₁² + 4 = X₂² + 4

x₁ = x₂

∴ f (x) is one-one

Let y = f(x) y = 4x + 3

x = y - 3/4 ∈R₊

∴ f (x) is onto

Let f^-1 (x) = y

f(y) = x

4y +3 = x

y = x - 3/4

∴ f^-1 : [4,8) → R+ is defined by

f^-1 (x) = x - 3/4

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Let R+ be the set of all non- negative real numbers. Show that the function f: R+ → [4,∞) given by f(x) = x2 + 4 is invertible and write the inverse of f.

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