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Consider f : R+ → [4, ∞) given by f(x) = x2 + 4. Show that f is invertible with the inverse f–1 of f given by f–1(y) = √???? − ???? , where R+ is the set of all non-negative real numbers.
Consider f : R+ → [4, ∞) given by f(x) = x2 + 4. Show that f is invertible with the inverse f–1 of f given by f–1(y) = √???? − ???? , where R+ is the set of all non-negative real numbers.
CBSE | Class 12 | Exercise 1.3 | Maths | NCERT | Relations and Functions
Consider f : R+ → [4, ∞) given by f(x) = x2 + 4. Show that f is invertible with the inverse f–1 of f given by f–1(y) = √???? − ???? , where R+ is the set of all non-negative real numbers.

solution:

Think about f : R+ → [4, ∞) given by f(x) = x2 + 4 Let x, y ∈ R → [4, ∞) then, at that point

f(x) = x2 + 4 and

f(y) = y2 + 4

on the off chance that f(x) = f(y) x2 + 4 = y2 + 4 or x = y

f is one-one.

Presently y = f(x) = x2 + 4 or x = √???? − 4 as x > 0 f(√???? − 4 )= (√???? − 4 )^2 + 4 = y

f(x) = y

f is onto work.

Consequently, f is invertible and Inverse of f will be f – 1 (y) = √???? − 4 .

i

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