Suppose f(x)=2x-5 and g(x)=|-3x-1|. find the following value. g(2)-f(0)=

Hello!

To find the value of of g(2) - f(0), we need to substitute "2" into g(x), and "0" into f(x).

This is how it would look after substituting: f(0) = 2(0) - 5 and g(2) = |-3(2) - 1|. Also, since the expression says we are subtracting f(x), the entire equation becomes negative: -f(0) = -(2(0) - 5).

With that, we can solve for the final value.

|-3(2) - 1| + -(2(0) - 5) (multiply)

|-6 - 1| + -(0 - 5) (use the distributive property)

|-6 - 1| + 5 (simplify)

|-7| + 5 (simplify the absolute value of -7)

7 + 5 = 12

Therefore, g(2) - f(0) is equal to 12.