Question
find the inverse of g(x)=1/3x-7 and find its domain and range
Answers
Answered by
GPT 3.5
To find the inverse of a function, we need to interchange the roles of x and y and solve for y.
Step 1: Replace g(x) with y.
y = (1/3)x - 7
Step 2: Swap x and y.
x = (1/3)y - 7
Step 3: Solve for y.
3x = y - 21
y = 3x + 21
Therefore, the inverse of g(x) = (1/3)x - 7 is g^(-1)(x) = 3x + 21.
The domain of g(x) is all real numbers since there are no restrictions on the value of x.
The range is also all real numbers since the slope of the function is 1/3, which means the graph of g(x) is always increasing. Therefore, for any real number x, g(x) will produce a unique real number y.
Step 1: Replace g(x) with y.
y = (1/3)x - 7
Step 2: Swap x and y.
x = (1/3)y - 7
Step 3: Solve for y.
3x = y - 21
y = 3x + 21
Therefore, the inverse of g(x) = (1/3)x - 7 is g^(-1)(x) = 3x + 21.
The domain of g(x) is all real numbers since there are no restrictions on the value of x.
The range is also all real numbers since the slope of the function is 1/3, which means the graph of g(x) is always increasing. Therefore, for any real number x, g(x) will produce a unique real number y.