Answer:

Step-by-step explanation:
Given function,

Step 1 : Replace g(x) by y:

Step 2 : Swap x and y:

Step 3 : Solve the equation for y ( isolate y in the left side ):





Step 4: Replace y by
:

Hence, the inverse of the function g(x) is
.
Answer:
8a. x = 16√3
8b. y = 8√3
Step-by-step explanation:
8a. Determination of the value of x
Adjacent = 24
Hypothenus = x
Angle θ = 30°
The value of x can be obtained by using cosine ratio as illustrated below:
Cos θ = Adjacent /Hypothenus
Cos 30 = 24 / x
√3/2 = 24/x
Cross multiply
x × √3 = 2× 24
x × √3 = 48
Divide both side by √3
x = 48/√3
Rationalise
x = 48/√3 × √3/√3
x = 48√3 / √3 × √3
x = 48√3 / 3
x = 16√3
8b. Determination of the value of y
Opposite = y
Adjacent = 24
Angle θ = 30°
The value of y can be obtained by using Tan ratio as illustrated below:
Tan θ = Opposite / Adjacent
Tan 30 = y / 24
1 / √3 = y /24
Cross multiply
y × √3 = 1 × 24
y × √3 = 24
Divide both side by √3
y = 24 /√3
Rationalise
y = 24 /√3 × √3/√3
y = 24 ×√3 / √3 × √3
y = 24√3 / 3
y = 8√3
<span>Amount
of Rice (cups) Amount of Water (cups)
2 5
3 7.5
5 12.5
8 20
Let's find the ratio of rice and water:
5 / 2 = 2.5 => 2 * 5 = 5
7.5 / 3 = 2.5 => 3 * 2.5 = 7
12.5 / 5 = 2.5 => 5 * 2.5 = 12.5
20 / 8 = 2.5 => 8 * 2.5 = 20
So, as the ratio of water ot rice is constant, and the first variable is the amount of rice, you can calculate the amount of water given the amount of rice.
So, the amount of rice is independent value and the amount of water is dependent (it depends on the amount of rice).
The amount of rice is
the dependent value. FALSE
The amount of water is the dependent value.TRUE
The
amount of rice is the independent value. TRUE
The amount of water is the
independent value.</span>FALSE
(1/2) ^2 = 1/2 * 1/2 = 1/4
1/4 < 1/2
It’s just y= 17x. There’s nothing added or subtracted, or else it wouldn’t be (0,0).