Search any question & find its solution
Question:
Answered & Verified by Expert
If $f(x)$ is a real valued function defined by
$f(x)=\frac{a x^{10}+b x^8+c x^6+d x^4+e x^2+12 x+15}{x}$
$(x \neq 0)$ and $f(4)=-4$, then $f(-4)=$
Options:
$f(x)=\frac{a x^{10}+b x^8+c x^6+d x^4+e x^2+12 x+15}{x}$
$(x \neq 0)$ and $f(4)=-4$, then $f(-4)=$
Solution:
1928 Upvotes
Verified Answer
The correct answer is:
28
$f(x)=\frac{a x^{10}+b x^8+c x^6+d x^4+e x^2+12 x+15}{x}$
and $f(4)=-4$
$\because f(x)=a x^9+b x^7+c x^5+d x^3+e x+12+\frac{15}{x}$
$\therefore f(-x)=-a x^9-b x^7-c x^5-d x^3-e x+12-\frac{15}{x}$
$\therefore f(x)=f(-x)=24$
$\begin{aligned} & f(4)+f(-4)=24 \\ & f(-4)=24-f(4) \\ & =24-(-4)=28\end{aligned}$
and $f(4)=-4$
$\because f(x)=a x^9+b x^7+c x^5+d x^3+e x+12+\frac{15}{x}$
$\therefore f(-x)=-a x^9-b x^7-c x^5-d x^3-e x+12-\frac{15}{x}$
$\therefore f(x)=f(-x)=24$
$\begin{aligned} & f(4)+f(-4)=24 \\ & f(-4)=24-f(4) \\ & =24-(-4)=28\end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.