Question

Find the inverse of g(x)=1/3x - 7 and then find its domain and range.

Please help. Thank you.

Answer 1

all work is pictured and shown

the domain and range are all real numbers

Answer 2

Domain = (-∞, ∞)

Range = (-∞, ∞)

Inverse Function: x = 3(y + 7)

Explanation:

The Domain is the all possible input values of a function that gives defined values.

The Range is the all defined output values that we get from a function (or y).

Here if we kept all real number for "x" that gives defined values of y.

So, Domain is all real number i.e. (-∞, ∞)

Similarly, Range = (-∞, ∞)

Inverse of g(x) :

`\text{Let}\ y = (1)/(3)x -7\\ \Rightarrow y = (x)/(3)-7\\ \Rightarrow y +7= (x)/(3)\\\Rightarrow 3(y +7)= x`

Hence, Inverse Function of g(x) is: x = 3(y + 7)