Question

Find value of :
$\huge \boxed {f\left(x\right)=2x+3,\:g\left(x\right)=-x^2+5,\:\left(f\:\left(g\left(x\right)\right)\right)}$

Only Math Aryabhata's or stars, mods are
allowed

Answer 1

$\bf{Question:}$

$\bf{f\left(x\right)=2x+3,\:g\left(x\right)=-x^2+5,\:\left(f\:\left(g\left(x\right)\right)\right)}$

$\bf{Answer:}$

$\sf{f=2x+3,\:g=-x^2+5,\:\left(f\left(x\right)\:\circ \:g\left(x\right)\right):\quad -2x^2+13}$

Steps :

$\mathrm{For}\:f=2x+3\:\mathrm{substitute}\:x\:\mathrm{with}\:g\left(x\right)=-x^2+5$

$=2\left(-x^2+5\right)+3$

$\mathrm{Expand}\:2\left(-x^2+5\right)+3:\quad -2x^2+13$

$=-2x^2+13$

Answer 2

$\mathrm{Expand}\:2\left(-x^2+5\right)+3:\quad -2x^2+13$$\mathrm{Add\:the\:numbers:}\:10+3=13$$=-2x^2+13$$=-2x^2+13$