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Which function is the inverse of f(x)=x²-16 if the domain is f(x)>0?​

Which function is the inverse of f(x)=x²-16 if the domain is f(x)>0?​-example-1

2 Answers

4 votes

Answer:


f^(-1)(x)=√(x+16)

Explanation:


f(x)=x^2-16

The inverse of the function
f is
f^(-1)

The Range of the inverse function
f will be the Domain of the function
f


Ran(f^(-1)) = [0, \infty)

The inverse of


f(x)=x^2-16

is


f^(-1)(x)=√(x+16)

Note that if the domain of the function
f where all the Real numbers, the inverse would be


f^(-1)(x)=\pm√(x+16)

User Mark Renouf
by
5.4k points
5 votes

Answer:

Inverse of
f(x)=x^2-16 is
f^(-1)(x)=√(x+16)

Option A is correct option.

Explanation:

We need to find inverse of
f(x)=x^2-16

For finding inverse replace f(x) with y


y=x^2-16

Now, solve for x

Adding 16 on both sides


y+16=x^2-16+16\\y+16=x^2\\=> x^2=y+16

Taking square root on both sides:


x^2=y+16\\√(x^2) =√(y+16) \\x=√(y+16)

Now replace x with f^{-1}(x) and y with x


f^(-1)(x)=√(x+16)

So, inverse of
f(x)=x^2-16 is
f^(-1)(x)=√(x+16)

Option A is correct option.

User Lmpeixoto
by
5.1k points