Question

If ​f(x)=x^2- 4 and ​g(x)=x^2 plus 2 x​,

​(c)​ (f-​g)(-1/3) ​= ? (Simplify your​ answer.)

Answer 1

`\huge\boxed{(f-g)\left(-(1)/(3)\right)=-3(1)/(3)}`

Explanation:

`\text{We have}:\\\\f(x)=x^2-4\ \text{and}\ g(x)=x^2+2x\\\\(f-g)(x)=f(x)-g(x)\\\\\text{therefore}\\\\(f-g)(x)=(x^2-4)-(x^2+2x)=x^2-4-x^2-2x\\\\=(x^2-x^2)-2x-4=-2x-4\\\\(f-g)\left(-(1)/(3)\right)\to\text{put}\ x=-(1)/(3)\ \text{to the equation of the function}\ (f-g)(x):\\\\(f-g)\left(-(1)/(3)\right)=-2\left(-(1)/(3)\right)-4=(2)/(3)-4=-3(1)/(3)`