Final answer:
g(−2) = 16
g(-1/2) = 2
g(0) = 1
g(3/2) = 8
Step-by-step explanation:
1) To find g(-2), we need to substitute -2 in place of x in the function g(x) = (1/4)^x.
So, g(-2) = (1/4)^(-2).
To evaluate this, we can write it as 1/(1/4)^2.
Simplifying further, we get 1/(1/16) = 16.
Therefore, g(-2) = 16.
2) To find g(-1/2), we substitute -1/2 in place of x in the function g(x) = (1/4)^x.
So, g(-1/2) = (1/4)^(-1/2).
To evaluate this, we can write it as the square root of 1/(1/4), which simplifies to the square root of 4, which is 2.
Therefore, g(-1/2) = 2.
3) To find g(0), we substitute 0 in place of x in the function g(x) = (1/4)^x.
So, g(0) = (1/4)^0.
Any number raised to the power of 0 is 1.
Therefore, g(0) = 1.
4) To find g(3/2), we substitute 3/2 in place of x in the function g(x) = (1/4)^x.
So, g(3/2) = (1/4)^(3/2).
To evaluate this, we can take the square root of (1/4)^3, which simplifies to (1/4)^3/2 = (1/4)^1.5 = 1/(sqrt(1/4)^3).
Simplifying further, we get 1/(1/8) = 8.
Therefore, g(3/2) = 8.