Will pick best answer..right answer.help.?

Question

Find the linear function f(x) satisfying f(-7)= -10 and the point ( 1 , -5 ) is on the graph of the inverse of f.

What is the answer and how do you go about solving this type of question.

Thank you.

Answer 1

(-7,-10)    (-5,1)   slope=1--10/-5--7=11/2=5.5

y--10=5.5(x--10)         y+10=5.5x+55        y=5.5x+45

Answer 2

It's easy to find the equation of a line if you have two points on the line. So let's find two points:

First, f(-7) = -10 means that the point (-7,-10) is on the line.

Then if (1,-5) is on the graph of the inverse of f, f^-1, we have that f^-1(1) = -5. This means that if you plug -5 into f, you get 1, hence f(-5) = 1. Thus the point (-5,1) is on the line.

Now that you have your two points, all you have to do it find the slope:

m = (1 - -10) / (-5 - -7) = 11 / 2.

Using the point-slope formula for a line, we see that the line is given by the equation

y - 1 = 11/2 (x + 5).

Or solving for y,

f(x) = 11/2(x+5) + 1

You can simplify this if you want. Hope this helps.