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

Let f:NN be a function defined as f(x)=9x2+6x5. Show that f:NS, where S is the range of f, is invertible. Find the inverse of f and hence find f1(43) and f1(163)

Open in App
Solution

f(x)=9x2+6x5
x=6±36+18018=1±63
Approximate value of these values is 0.466,1.15
Thus, for all the natural numbers, the value of the function will be positive and hence, its bijective. Its inverse is thus possible.
Let f(x) be y.
We get 9x2+6x5y=0
x=6±36+180+36y18=1±y+63
Or, f1x=1±x+63
f1(43)=1±73=2 (negative value discarded)
f1(163)=1±133=4 (negative value discarded)

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