Inverse function values

Hello again!

I've been posting a lot of questions recently and I just wanted to let you know that I truly appreciate it! I'm doing some power studying and am forgetting all of these things now that it's summer. Grarrrhh... I got another one for you...

The function f above has an inverse function for which of the following values of a and b?

Answer: a= -1, b = -2

Now, I know how to find the inverse of a function. Basically, you flip the x and y values and then try and put it back into the y= form. But I'm lost about the whole values thing... could somebody explain to me how they arrived at that answer?

Thanks for the very helpful post. However, on this test they ("the proctors") won't provide a graphing calculator (it's actually disallowed). Because of this, I would need to know how to solve it algebraically? How do you solve this algebraically?

Thanks for the very helpful post. However, on this test they ("the proctors") won't provide a graphing calculator (it's actually disallowed). Because of this, I would need to know how to solve it algebraically? How do you solve this algebraically?

I didnt ask you to use a graphing calculator. The equations are equations of a parabola and a straight line. Dont you know to plot these things ?

To answer this problem you need to recognize that y=ax+b defines a line with slope a and y-intercept at b. For the inverse of a function to be a function there must be a unique value of x associated with each y. Given that for x<0 covers the range , that means that the y=ax+b part must be limited to 0 and negative numbers. Therore a must be negative, and b must be 0 or negative. Hence the answer.