Let g(x) = 10-x/2+x
a. Find g(-1)
b. state the domain of the function
10-x/2+x
c. Find g (t + 1) and simplify as much as possible
To find the value of g(-1), we need to substitute -1 into the function g(x).
a. g(x) = 10 - x/2 + x
Replacing x with -1:
g(-1) = 10 - (-1)/2 + (-1)
= 10 + 1/2 - 1
= 10 + 0.5 - 1
= 10.5 - 1
= 9.5
Therefore, g(-1) = 9.5.
To state the domain of the function g(x) = 10 - x/2 + x, we need to determine which values of x are allowed. The domain is the set of all possible input values that the function can accept.
b. In this case, there are no restrictions on the domain of g(x). The function g(x) is defined for all real numbers. Therefore, the domain of g(x) is (-∞, +∞), which means any real number is allowed as an input.
To find g(t + 1) and simplify as much as possible, we substitute t + 1 into the function g(x) and simplify the expression.
c. g(x) = 10 - x/2 + x
Replacing x with (t + 1):
g(t + 1) = 10 - (t + 1)/2 + (t + 1)
Expanding and simplifying:
g(t + 1) = 10 - (t/2 + 1/2) + (t + 1)
= 10 - t/2 - 1/2 + t + 1
Combining like terms:
g(t + 1) = (10 + 1) + (t - t/2)
= 11 + (2t - t)/2
Simplifying further:
g(t + 1) = 11 + t/2
Therefore, g(t + 1) simplifies to 11 + t/2.