Question

1 . Let ƒ(x) = g(x) = (1/4)^x. Find g(−2).

2. Let ƒ(x) = g(x) = (1/4)^x. Find g(-1/2)
3. Let ƒ(x) = g(x) = (1/4)^x. Find g(0)
4. Let ƒ(x) = g(x) = (1/4)^x. Find g(3/2)​

Answer 1

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.