let the function g be defined by
g(x)=1-5x if the domain of the function of g is {x-3 is less than or equal to x which is less than or equal to 2} what is the smallest value of the range
show work please
To find the smallest value of the range of the function g, we need to determine the minimum value that g(x) can attain within its given domain.
The domain of g is defined as {x-3 ≤ x ≤ 2}. Let's find the minimum value of g(x) by evaluating g(x) at the boundary points of its domain.
Substituting the lower bound x = x-3 into the function, we have:
g(x-3) = 1 - 5(x-3)
= 1 - 5x + 15
= 16 - 5x
Substituting the upper bound x = 2 into the function, we have:
g(2) = 1 - 5(2)
= 1 - 10
= -9
Now we have two values of g(x). Comparing the two, we see that 16 - 5x will have a larger value than -9 within the given domain since it has a positive slope (a negative coefficient for x). Therefore, the minimum value of the range is -9.
Thus, the smallest value of the range of function g is -9.