Question

Find the inverse of the function, no solutions doesn't work and things like sqrt(9-x^2) doesn't either.

Answer 1

Answer:

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Answer 2

$\sf f(x)= \sqrt{9-x^2}$

• This function has a range of  $\begin{bmatrix}\sf{Range:}\:&\:0\le \:f\left(x\right)\le \:3\:\\ \:\sf{Interval\:Notation:}&\:\left[0,\:3\right]\end{bmatrix}$

To find inverse, make x the subject.

$\hookrightarrow \sf f(x)= \sqrt{9-x^2}$

$\hookrightarrow \sf y= \sqrt{9-x^2}$

$\hookrightarrow \sf y^2= 9-x^2$

$\hookrightarrow \sf -x^2 = y^2-9$

$\hookrightarrow \sf x^2 = -y^2+9$

$\hookrightarrow \sf x =\pm \sqrt{9-y^2}$

$\hookrightarrow \sf f^{-1}(x) = \pm \sqrt{9-x^2}$

the inverse has domain :  $\begin{bmatrix}\sf{Domain:}\:&\:-3\le \:x\le \:3\:\\ \:\sf{Interval\:Notation:}&\:\left[-3,\:3\right]\end{bmatrix}$