or the following function defined that is one-to-one, write an equation for the inverse function in the form , a
nction is not one-to-one, say so.

A.
B.
C. The function is not one-to-one.

Ask by Parry Stewart. in the United States

Nov 05,2024

Question

or the following function defined that is one-to-one, write an equation for the inverse function in the form , a
nction is not one-to-one, say so.

A.
B.
C. The function is not one-to-one.

Ask by Parry Stewart. in the United States

Nov 05,2024

UpStudy AI · Accepted Answer

To find the inverse function of $$ f(x) = \sqrt{-5+x} $$ for $$ x \geq 5 $$, we need to follow these steps:

1. Replace $$ f(x) $$ with $$ y $$ to get the equation in terms of $$ y $$: $$ y = \sqrt{-5+x} $$.
2. Swap $$ x $$ and $$ y $$ to get the inverse function in terms of $$ x $$: $$ x = \sqrt{-5+y} $$.
3. Solve for $$ y $$ to find the inverse function $$ f^{-1}(x) $$.

Let's proceed with these steps.
Solve the equation by following steps:
- step0: Solve for $$y$$:
  $$x=\sqrt{-5+y}$$
- step1: Swap the sides:
  $$\sqrt{-5+y}=x$$
- step2: Raise both sides to the $$2$$-th power$$:$$
  $$\left(\sqrt{-5+y}\right)^{2}=x^{2}$$
- step3: Evaluate the power:
  $$-5+y=x^{2}$$
- step4: Move the constant to the right side:
  $$y=x^{2}+5$$
The inverse function of $$ f(x) = \sqrt{-5+x} $$ for $$ x \geq 5 $$ is $$ f^{-1}(x) = x^2 + 5 $$.

Therefore, the correct answer is:
A. $$ f^{-1}(x) = x^2 + 5, x \geq 0 $$
A. $$ f^{-1}(x) = x^2 + 5, x \geq 0 $$

or the following function defined that is one-to-one, write an equation for the inverse function in the form , a
nction is not one-to-one, say so.

A.
B.
C. The function is not one-to-one.

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or the following function defined that is one-to-one, write an equation for the inverse function in the form , a nction is not one-to-one, say so. A. B. C. The function is not one-to-one.

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or the following function defined that is one-to-one, write an equation for the inverse function in the form , a
nction is not one-to-one, say so.

A.
B.
C. The function is not one-to-one.