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`

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`