Find the inverse the function and the domain and the range of f and f^(-1)

vestirme4

vestirme4

Answered question

2021-10-29

Find the inverse the function and the domain and the range of f and f1, if the function is f(x)=2xx+5 and it's one-to-one.

Answer & Explanation

Sally Cresswell

Sally Cresswell

Skilled2021-10-30Added 91 answers

To find the inverse function, substitute x=f1andy=x and calculate:
y=2xx+5
xy+5y=2x
x(y2)=5y
x=5y2y
x=5y2y
f1(x)=5x2x
If f(f1(x))=f1(f(x)),
then f1(x) is an inverse function of f(x)
=f(f1(x))
=f(5x2y)
=2×5x2y5x2x+5
=10x2x5x+105x2x
=x
The domain of f(x) is range for f1(x)
And, the range of f(x) is domain for f1(x)
f(x)=2xx+5
x+5=0
x=-5
Domain =(,5)(5,)
f1(x)=5x2x
2-x=0
x=2
Range =(,2)(2,)

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