If-f-2x-x-2-4x-1-what-all-values-of-t-for-which-f-t-2-11-4-where-f-represents-a-function-

Question Number 115854 by bemath last updated on 29/Sep/20

I f f (2 x) = x^{2} + 4 x + 1, w h a t a l l

v a l u e s o f t f o r w h i c h f (\frac{t}{2}) = - \frac{11}{4}

w h e r e f r e p r e s e n t s a f u n c t i o n

Answered by bobhans last updated on 29/Sep/20

\Leftrightarrow f (x) = {(\frac{x}{2})}^{2} + 4 (\frac{x}{2}) + 1

\Leftrightarrow f (\frac{t}{2}) = {(\frac{t}{4})}^{2} + 4 (\frac{t}{4}) + 1 = - \frac{11}{4}

\Rightarrow \frac{t^{2}}{16} + \frac{4 t}{4} + \frac{15}{4} = 0

\Rightarrow t^{2} + 16 t + 60 = 0

\Rightarrow (t + 6) (t + 10) = 0 \to {\begin{cases} t = - 6 \\ t = - 10 \end{cases}

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