Question

If $f\left(y\right)=-y^2+2y-6$,the value of $f\left(-2y\right)+f\left(-y\right)=?$

• A. $-5y^2-6y-12$
• B. $-2y^2-3y+10$
• C. $8y^2+2y-9$
• D. $-3y^2-6y+14$

Answer 1

The correct option is A $-5y^2-6y-12$

Given function:

$f\left(y\right)=-y^2+2y-6.....\left(1\right)$

for calculating $f(-2y)$ put $y=-2y$ in equation (1) we get

$f(-2y)=-(-2y{)}^2+2(-2y)-6$

$f(-2y)=-4y^2-4y-6....\left(2\right)$

for calculating $f(-y)$ put $y=-y$ in equation (1) we get

$f(-y)=-(-y{)}^2+2(-y)-6$

$f(-y)=-y^2-2y-6....\left(3\right)$

add equation (2) and (3) we get

$f(-2y)+f(-y)=-4y^2-4y-6-y^2-2y-6$

$f(-2y)+f(-y)=-5y^2-6y-12...\left(4\right)$