Determine-the-values-of-m-R-for-which-the-function-f-x-1-2x-2-mx-m-is-the-set-of-real-numbers-

Question Number 74265 by Maclaurin Stickker last updated on 21/Nov/19

D e t e r m i n e t h e v a l u e s o f m \in R f o r

w h i c h t h e f u n c t i o n f (x) = \frac{1}{\sqrt{2 x^{2} - m x + m}}

i s t h e s e t o f r e a l n u m b e r s .

Answered by MJS last updated on 21/Nov/19

2 x^{2} - m x + m = 0

x = \frac{m \pm \sqrt{m (m - 8)}}{4}

to get no zeros :

m (m - 8) < 0

\Rightarrow 0 < m < 8

for 0 < m < 8 : \forall x \in R : 2 x^{2} - m x + m > 0

in this case f (x) is defined for x \in R but the

range is 0 < f (x) ⩽ \frac{2 \sqrt{2}}{\sqrt{8 m - m^{2}}}

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