Question

Evaluate the function f(x)=x^2+2x+3 at the given values of the independent variable and simplivy
f(-9)

f(x+1)

f(-x)

Answer 1

Answer: i) f(-9)= 66

ii) $f(x+1)=x^2+4x+6$.

iii) $f(-x)=x^2-2x+3$

Step-by-step explanation:

The given function : $f(x)=x^2+2x+3$.

i) For f(-9) , the independent variable is x= -9.

Put x= -9 in given function , we get

$f(-9)=(-9)^2+2(-9)+3$

$=81-18+3=66$

Thus ,  f(-9)= 66

ii) For f(x+1) , the independent variable is x= x+1.

Replace x  by x+1 in given function , we get

$f(x+1)=(x+1)^2+2(x+1)+3$.

$=(x^2+1+2x)+2x+2+3$  $[\because\ (a+b)^2=(a^2+b^2+2ab)]$

$=x^2+1+2x+2x+5$

$=x^2+4x+6$

Thus ,  $f(x+1)=x^2+4x+6$.

iii)For f(-x) ,  the independent variable is x=-x.

Replace x  by -x in given function , we get

$f(-x)=(-x)^2+2(-x)+3$.

$=x^2-2x+3$  [∵ (+)(-)=(-)]

Thus , $f(-x)=x^2-2x+3$