Question

Given the functions: f(x)=3x,g(x)=|x-2|,h(x)=(1)/(x+6) Evaluate the function (g-h)(-5) for the given value of x.

Answer 1

To evaluate (g-h)(-5), calculate g(-5) and h(-5) separately. Perform the subtraction g(-5) - h(-5), which equals 7 - 1. The final result is 6.

Step-by-step explanation:

The student asked to evaluate the function (g-h)(-5) where g(x) is the absolute value function g(x)=|x-2| and h(x) is the reciprocal function h(x)=(1)/(x+6). To find (g-h)(x), we need to subtract h(x) from g(x).

• First, evaluate g(-5): g(-5)=|-5-2|=|(-7)|=7.
• Next, evaluate h(-5): h(-5)=(1)/(-5+6)=(1)/1=1.
• Now, subtract h(-5) from g(-5): (g-h)(-5)=g(-5)-h(-5)=7-1=6.

The value of (g-h)(-5) is 6.