Question

Find the inverse of g(x)=1/3x - 7 and then find its domain and range if you can show steps that would be gladly appreciated thank you so much

Answer 1

g-1(x) = 3(x + 7).

Domain is All Real values of x.

Range is All Real values of the function.

Step-by-step explanation:

Let y = 1/3 x - 7

1/3 x = y + 7

Multiply both sides by 3:

x = 3(y + 7)

So the inverse of g(x) = g-1(x) = 3(x + 7).

Domain is All Real values of x.

Range is All Real values of the function.

Answer 2

To find the inverse of g(x)=1/3x - 7, interchange x and y and solve for y. The inverse of g(x) is g^-1(x) = 3x + 21. The domain and range of g(x) are (-∞, ∞).

Step-by-step explanation:

To find the inverse of the function g(x) = 1/3x - 7, we need to interchange x and y and solve for y.

1. Replace g(x) with y: y = 1/3x - 7
2. Interchange x and y: x = 1/3y - 7
3. Solve for y: x + 7 = 1/3y
4. Multiply both sides by 3: 3(x + 7) = y
5. Simplify: 3x + 21 = y

So, the inverse of g(x) is g-1(x) = 3x + 21.

The domain of g(x) is the set of all possible x-values for which the function is defined. Since g(x) is defined for all real numbers, the domain is (-∞, ∞).

The range of g(x) is the set of all possible y-values that the function can take on. Since the function is a linear equation, the range is also all real numbers (-∞, ∞).