For the function $f(x)=\sqrt{x^{2}-8 x+24}-1$, find all values $x$ for which $f(x)=2$.
A) $\{3,-5\}$
B) $\{-3,-5\}$.
C) $\{3,5\}$
D) $\varnothing$

Question

Quizplus · Accepted Answer

To find the values of $x$ for which $f(x) = 2$, we set the function equal to 2 and solve for $x$:$$\sqrt{x^{2}-8x+24} - 1 = 2 \implies \sqrt{x^{2}-8x+24} = 3$$Squaring both sides gives:$$x^{2} - 8x + 24 = 9$$Simplifying:$$x^{2} - 8x + 15 = 0$$Factoring the quadratic equation:$$(x - 3)(x - 5) = 0$$Thus, $x = 3$ or $x = 5$, which corresponds to choice C.

For the Function f(x)=x2−8x+24−1f(x)=\sqrt{x^{2}-8 x+24}-1f(x)=x2−8x+24​−1 , Find All Values xxx For Which f(x)=2f(x)=2f(x)=2

For the Function $f(x)=\sqrt{x^{2}-8 x+24}-1$ , Find All Values $x$ For Which $f(x)=2$