Question

Given that f(x)= {2}" alt="\frac{x^{2}-3 }{2}" align="absmiddle" class="latex-formula">
A) Find $f^{-1}(x)$
B) Find $f^{-1} (11)$
Separate your 2 answers for part B with a comma.
I've solved $f^{-1}(x)$, which was $\sqrt{2x+3}$

However after this I do not see how I can get another value other than 5.

Answer 1

Answer:

$x=5,-5$

Step-by-step explanation:

$\\ y=\frac{x^2-3}{2}\\\\ x=\frac{y^2-3}{2}\\\\ 2x=y^2-3\\\\ y^2=2x+3\\\\ f^{-1}(x)=\pm\sqrt{2x+3}\\\\ f^{-1}(x)=\pm\sqrt{2(11)+3}\\=\pm\sqrt{25}=\pm 5$