wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If f : R → R be defined by f(x) = x3 −3, then prove that f−1 exists and find a formula for f−1. Hence, find f−1 (24) and f−1 (5).

Open in App
Solution

Injectivity of f :
Let x and y be two elements in domain (R),

such that, x3-3=y3-3 x3=y3 x=y
So, f is one-one.

Surjectivity of f :
Let y be in the co-domain (R) such that f(x) = y

x3-3=yx3=y+3x=y+33R

f is onto.
So, f is a bijection and, hence, it is invertible.

Finding f -1:
Let f-1x=y ...1x=fyx=y3-3x+3=y3y=x+33 = f-1x [from 1]So, f-1x=x+33 Now, f-124=24+33=273=333=3 and f-15=5+33=83=233=2

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Continuity of Composite Functions
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon