Question

For f(x)=3x+1 and g(x)=x^2-6, fine (f-g)(x)

Answer 1

`\large\boxed{(f-g)(x)=-x^2+3x+7}`

Explanation:

`(f-g)(x)=f(x)-g(x)\\\\f(x)=3x+1,\ g(x)=x^2-6\\\\\text{Substitute:}\\\\(f-g)(x)=(3x+1)-(x^2-6)\\\\(f-g)(x)=3x+1-x^2-(-6)\\\\(f-g)(x)=3x+1-x^2+6\\\\(f-g)(x)=-x^2+3x+(1+6)\\\\(f-g)(x)=-x^2+3x+7`

Answer 2

= -x^2 +3x+7

Explanation:

f-g(x)

means to subtract g(x) from f(x)

f(x)- g(x)=3x+1 -(x^2-6)

Distribute the minus sign

f(x)-g(x)= 3x+1 -x^2 +6

= 3x+7-x^2

= -x^2 +3x+7