Q. 115.0( 2 Votes )

Consider f : R<su

Answer :

A function is said to be invertible if it is one-one onto.

To prove that f(x) is invertible we need to prove that it is one-one onto.

As f(x) = x2 + 4

And domain is all non-negative real numbers.

No two values of x is going to give same results as x is a non-negative.

So for every unique value of x there is only one unique value of f(x)

Hence, we say that f(x) is one – one.

f(x) = x2 + 4 ≥ 4

range of f(x) = [4, ∞)

As, f : R+ [4, ∞) [given mapping of f]

Range = [4,∞) = co-domain

f(x) is onto

As, f(x) is one-one and onto.

f(x) is invertible.

Now, we need to find the inverse of the function f(x)

Let, y = x2 + 4

x2 = y – 4

x = ± √(y-4)

As domain of f is [0,∞) {given}

x > 0

x = √(y-4)

Or we can write: f-1(y) = √(y-4)

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses

| Let * be a binaMathematics - Board Papers

Find the idMathematics - Board Papers

Let f : A Mathematics - Exemplar

Show that the binMathematics - Board Papers

Determine whetherRD Sharma - Volume 1

Fill in theMathematics - Exemplar