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Question

For the function f:RR,f(x)=3x+2, if f1, exists then find f1(x).

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Solution

Inverse of a function exists if it is both one-one and onto.
Checking for one-one:

if f(x1)=f(x2)

3x1+2=3x2+2

x1=x2

Hence , f(x) is one-one

Co-domain of f(x) is R
And, we know that 3x+2 is a straight line graph and hence its range is R

Since, range = co-domain , hence f(x) is onto as well.

Hence, f(x) is invertible.

Now, y=f(x)=3x+2

x=y23

And, x=f1(y)

f1(y)=y23

Replacing y with x-

f1(x)=x23


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