How do you find the inverse of $f (x) = x^{2} - 2$ $f(x)=x^2-2$ from $x \leq 0$ $x<=0$ and graph both f and $f^{- 1}$ $f^-1$ ?

Question

How do you find the inverse of $f (x) = x^{2} - 2$ $f(x)=x^2-2$ from $x \leq 0$ $x<=0$ and graph both f and $f^{- 1}$ $f^-1$ ?

1 Answer

Impact of this question

14100 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-09-05T02:10:40

See below.

Explanation:

To find the inverse of a function, you can switch the $x$ $x$ and $y$ $y$ variables and solve for $y$ $y$ .

$y = x^{2} - 2$ $y=x^2 - 2$

$x = y^{2} - 2$ $x = y^2 - 2$ $\to$ $->$ switch variables

$x + 2 = y^{2}$ $x+2 = y^2$

$y = \pm \sqrt{x + 2}$ $y = +- sqrt (x+2)$

However, since $f (x)$ $f(x)$ is restricted to $x \leq 0$ $x<=0$ , $f^{- 1} (x)$ $f^(-1)(x)$ will be restricted to $y \leq 0$ $y<=0$ . We only take the negative result above.

$f^{- 1} (x) = - \sqrt{x + 2}$ $f^(-1)(x) = -sqrt(x+2)$

To graph $f (x)$ $f(x)$ , simply graph the parabola but keep only the negative $x$ $x$ -values.

![desmos.com]( useruploads.socratic.org )

To graph $f^{- 1} (x)$ $f^(-1)(x)$ , graph $\sqrt{x}$ $sqrtx$ , then translate it $2$ $2$ units left and reflect it over the $x$ $x$ -axis.

![desmos.com]( useruploads.socratic.org )

If two functions are inverses, they should be reflections of each other over the line $y = x$ $y=x$ . The graph below confirms that they are indeed inverses.

![desmos.com]( useruploads.socratic.org )

Science

Math

Humanities

... and beyond

How do you find the inverse of $f (x) = x^{2} - 2$ $f(x)=x^2-2$ from $x \leq 0$ $x<=0$ and graph both f and $f^{- 1}$ $f^-1$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you find the inverse of f(x)=x2−2f(x)=x^2-2 from x≤0x<=0 and graph both f and f−1f^-1?

1 Answer

Explanation:

Related questions

Impact of this question

How do you find the inverse of $f (x) = x^{2} - 2$ $f(x)=x^2-2$ from $x \leq 0$ $x<=0$ and graph both f and $f^{- 1}$ $f^-1$ ?