Question 464355: For the function f (x) = 7x + 9, determine whether f (x) is one-to-one. If so, find the formula for the inverse and give the domain and range for f -1.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! For the function f (x) = 7x + 9, determine whether f (x) is one-to-one. If so, find the formula for the inverse and give the domain and range for f -1.
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f (x) = 7x + 9
By definition f(x) is one-to-one because for each x there is only one y-value. You can also see this if you note that the function is a straight line.
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To find its inverse, interchange x and y, then solve for y.
x=7y+9
7y=x-9
y=(x-9)/7=f-1
Domain: all real numbers (-∞,∞)
Range:also, all real numbers (-∞,∞)
note that this inverse is also a straight line
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